Tire selection for winter trike riding?
For bicycles the so called "snow tires" are essentially mountain bike tires with large gaps between the lugs so snow will come out.

Studded tires are intended for ice and do little good in loose snow. I have a snow bike (aka fat bike) with knobby tires designed for snow - but no studs.

I have another bike with Schwalbe Marathon 26"x2.2" studded tires and these are great on ice but are pretty much useless in snow more than 3" as they don't have a deep lugged design and they'll float on top of the snow where the studs cannot grip anything.

To recommend a tire I would need more information on wheel size, tire clearance and the riding conditions. For deep snow a knobby tire likely will work best. If you're encountering hard pack and ice then definitely consider studs.  

Also note that narrow tires will knife through loose snow better than wide tires which tend to float more.  So in some conditions a narrow (1.375") studded tire will perform better than a much wider 2.25" tire as the narrow tire will knife through the snow better for the studs to bite in.  Again, this is very dependent on the conditions.