As many have mentioned/eluded to, I wouldn't go venturing in conditions where it would be more than 6" of snow. Reason being as the previous poster also mentioned, hidden obstacles. But not only down trees, snow drifts can hide major holes, drop-offs from erosion, etc. Then there is the more likely aspect of snow drifts you are trying to go over and they are much deeper than you expect. This can easily result in getting high centered which is not the easiest situation to get out of even with multiple people with shovels.
I run snow on my utility ATV frequently and even that can be a major chore. We generally don't go out in conditions where the snow is deeper than 12" but again, we end up hitting drifts frequently, getting stuck and we are very experienced riders even in snow. When there are a couple of ATVs, we can link winches front or back and have anchor points as many times there is no solid tree within reach. I also carry 100' of winch rope (50' on the winch and a 2nd 50' rope) along with 20' tow strap, tree saver strap, snatch block, shackles, etc. I've used all of those as well. And keep in mind that is for a VERY capable Yamaha Grizzly ATV 4x4 with serious off-road, low pressure tires.
Out in CO, we are also confronted with mass amounts of snow in the high country this year and suspect the high country trails, 10,000+ feet will not be passable until mid-July or even later. Just better to find something lower for now as eventually, the snow will mostly melt off and allow some access.
I love me some land yachting