To most hunters out for waterfowl, woodcock, or maybe even grouse a snipe might be seen as an incidental. However, there are a few game birds that a snipe hunter might also encounter during his or her day afield. Knowing what they are and whether they are in season will be advantageous to the hunter that enjoys taking birds other than just the target species. In my state there is overlap between snipe season and that of a number of other game birds I encounter. Some very infrequently, others quite often. Among them are ducks, coots, rails, moorhens, dove, and woodcock. Depending on your location some of those might not be on your list and perhaps one or two others might need to be added.
Hunters targeting ducks probably account for more snipe taken as incidentals as any other hunters. That is because typically they are in areas where snipe are most likely to be. Also, most people I know that hunt snipe are also waterfowlers and they tend to be better at identifying snipe than the average upland hunter. To this day I am surprised by how many upland hunters not only can't identify a snipe but how many don't even know such a bird really exists. A bonus duck or two is a welcome addition to the game bag of a snipe hunter. This season past I had the opportunity to take a pair of Wood Ducks but had to pass since I was not shooting non-toxic shot. If you live in a state where non-toxic is required for snipe that isn't a problem. Since I live in a state where lead is legal for snipe that is what I always elect to shoot. That means unless I am planning a combo hunt and I also am willing to shoot snipe with non-toxic shot a duck as an incidental isn't an option for me.
I won't spend much time discussing Coots other than to mention them having a season that is likely to be open at the same time as snipe season. Very few people target them but the same rules that apply to ducks apply to them regarding non-toxic shot. I keep telling myself that one day I am going to bring a couple of Coots home. They have a lowly reputation more reflective of their lack of sporting qualities than their potential as table fare. Their diet is 100% vegetation which is more than I can say for a great number of ducks species that get much higher praise on the table.
There are four species of rails and you might have some or all of them where you hunt. I have seen three of the four myself when snipe hunting and taken two species as incidentals. The nearer you are to the coast you hunt the more likely you are to see rails. This is particularly true if you hunt tidal marshes along the coast. The rails include King, Clapper, Virginia, and Sora. Of them I have seen all but the King on the freshwater marshes where I hunt. The season for rails opens two months before snipe season but there is an overlap of about a month when both snipe and rails are legal. Rails are early migrants but if you hunt on their wintering grounds you might have them throughout the snipe season. On my last snipe hunt this past year in the middle of February I flushed a Virginia rail. Soras and Virginias are the smallest of the rails and are not quite as large as a snipe. When flushed, that is if you can get them to flush, they fly about as long as it takes for you to shoulder a gun. Last season I spent a few minutes trying to get a picture of a Virginia as he darted in and out of the grass. As soon as the camera would get focused he'd disappear only to reappear ten feet away. We played this game for a few minutes before I laughed a bit and put the camera away. I have shot and eaten more Soras than any of the other rails. They tsate like a dark meat bird and you will need at least as many of them for a meal as you would snipe. They are a bite-sized game bird. The law in my state will allow you to take twenty-five of either Virginia, Sora, or a combination of the two each day. I don't know of it is necessary to shoot that many of anything but you will need a few if you plan to feed more than one person. Clappers are not as common in the deep south as they are along the Atlantic coast but we get a few. They are larger than the other rails mentioned thus far, standing 12" high and having a wingspan up to 20". One of them will go a bit farther as part of a meal than the smaller rails but game laws are generally liberal with them as well. We can take fifteen per day here, not that I would want or need to. The last of the rails is the King. Slightly larger than the Clapper they stand 14" high with a wingspan reaching two feet across. They are similar to Clappers and a daily bag limit for the King is the same as the Clapper. You can take either fifteen of each or fifteen of the two as an aggregate. They have the reputation for being more likely to frequent freshwater marshes than Clappers. I have seen Clappers while hunting snipe around freshwater but never a King rail. As with anything, your results are liable to vary.
The next bird to mention is the Common Moorhen. I know people that call this bird the Florida Gallinule but we don't want to confuse it with the Purple Gallinule. Where you live the Purple Gallinule might be a legal gamebird but in my state it is protected. Our season for Moorhens runs concurrently with rail season so the overlap between it and snipe season is brief. It has been two decades since I have shot and eaten Moorhens but I will vouch for their palatability. Much of the lack of interest in them is for the same reason very few people pursue coots. It's more killing than it is hunting. For some reason the thought of game strictly as food isn't in vogue these days and that alone isn't justification to most people for pursuing some species. In some cases that is good. In others it isn't so good nor is it a valid reason not to give hunting and eating a particular species a try. With Moorhens I think many people might be pleasantly surprised.
What is there to say about Dove that you don't already know? Not much, so this will be brief. I just wanted to mention them because the season for them is likely to coincide with your snipe season and you might run into a few either in the field you are hunting snipe in or along the edge of a marsh where they might come for a drink and grit in the afternoon. Each season I see a few passing by and one or two added with a brace of snipe makes a nice mixed bag.
The last two Woodcock I shot at were seen while I was hunting snipe. The first one I bagged, the second one I didn't. While I hunt in the wide open unless I am in a corner where the woods are near the water I am not too likely to see a Woodcock during daylight hours. However, as I already mentioned it can occasionally happen. I acknowledge that many people don't hunt snipe in open marshes like I hunt so the odds of you encountering Woodcock might be as great or greater than they are of seeing a snipe. Our season for Woodcock is the last to open each year, it starting a full month-and-a half after snipe season which doesn't open until November. It is also the shortest season we have, running merely one month. Since I shoot very few Woodcock and haven't taken one in several years I consider them the prize trophy of unexpected surprises when it comes to incidentals while snipe hunting.
Are there other opportunities? Sure there are. I might see the occasional deer or turkey while out hunting snipe but I would not attempt to take one of them as an incidental and don't carry adequate loads for either when hunting snipe. For you anything might be fair game and a snipe hunt can turn into a rough shoot with anything from a rabbit to a quail or two thrown into the mix. There is something about variety and the surprise of adding that unexpected game to the bag that I find very appealing.