It depends a bit on how cold you expect it to be (winter riding or spring riding) and the duration of your exposure.
The snowmobile helmets work the best as they are designed to operate to any minimum temps you would be exposed to, keep your visor free and clear as they are heated and with some shrouding, keep the wind and air off you which keeps you warmer and minimizes the threat of frostbite.
The MX helmets and goggles can work well in moderate conditions of moderate duration as you can cover exposed skin with balaclavas, etc. Over time though, the high air flow, can cool you down excessively. Plenty of snowmobilers will use these as well in a very broad range of conditions, but the riding is different and there is much more stop and start, getting stuck, drinking
, etc. that breaks up the day.
Motorcycle helmets are fine down to a certain limit, and then don't have enough airflow to keep your visor clear. You can introduce more airflow by cracking your visor, but then you'll get cold pretty fast. Beyond that, you have to go to a snowmobile helmet.
Happy planning, where are you thinking of going?