Towing capacity isn't as much of an issue as most people would think. Snowmobile clutches are an extremely versatile system. Any adult-sized snowmobile made in the last 30 years has enough power to pull a equally-sized dead snowmobile with a rider on it. So, I wouldn't worry about power, if your main goal is ice fishing.
Last year, we saw a lot of snow on MN lakes - more than I can remember for a long time. Long track snowmobiles were the best for towing ice fishing shelters and sleds. Other years, I've crossed a lot of glare ice and studs made the difference.
So, I would say: fan-cooled (but there could be exceptions), longer than 121" track (136" or higher preferred), studded, good tow hitch.
Dave Genz is the complete gadget guy, and any snowmobile he uses is always loaded with cool stuff. I saw him at an ice show a couple of years ago sporting a Bearcat, but before that it was a Polaris 136, maybe Classic Touring, I don't remember.
Speaking of Polaris Classic Touring, that was the original purpose for mine. It was the last iteration of liquid cooling heat exchangers under the running boards. For whatever reason, that thing is extremely tolerant of low snow. I have yet to get it to overheat... knock on wood.