A few years ago I wanted something like this. Went out a bought a 2wd and put some chains on it. It worked on the ice and even with a "little" bit of snow. Any icy incline or snow and it was a 400+ pound shoreline ornament. I had a few good trips with it then it was more or less useless for ice fishing when we had more than 6" of snow and some snowpack on the shorelines.
A year or so later I figured I really need a sled since the snow was the primary issue when moving around out there with the ATV. Had a few good trips with it. But then learned that deep snow was a challenge and on bare ice with no picks in the track I was again a 400+ pound ornament on the ice. Just so happens that year was (2 years ago) was one of the real bad years for snowfall and we got buried (remember?).
I since sold both and have reverted back to what Jesus used for most his travels.
If you get an ATV and want to primarily use it for ice fishing reliably; get a 4WD. And the taller machines like Polaris Sportsman, Yamaha Grizzly, Arctic Cats, and other IRS machines will deal with the deeper snow better.
If you get a sled get something with reverse and a picked track. Long tracks will deal with towing gear better and generally a 2 seater (2up) will provide more gear carrying ability.
An ATV is good for year round use if you need it or have a place to ride. Registration is around $54 per year.
A sled is around $80 a year for registration but does have a limited season and don't forget that even though we have had some winters with lots of snow, there were years (about 10 years ago) when we had next to no snow and all rain. But it is really fun to drive a sled. My son preferred the snowmobile over the atv.
In NH, any atv or sled over 25 years old can be registered as an antique for $35 for life
My experience and 2 cents. Good luck!