i think for the trol, yoru better with the size you have, but buy new with bigger tread. You simply will not get "thin" tyres on a trol, they are too big and heavy. Its grip you want to think about for the snow, nice big tread to achieve this. Think of tractors, they have huge wheels, wide with massive grip obviously for deep mudded fields, similar principal for snow i think. As for snow on the roads, again thin tyres would be better, but that just isnt how it is, so its all about spreading that weight with as much grip as you can, and dont forget, if your tread digs away the snow so you actually touch tarmac, youre sorted, a normal tread wont, it will just slide on the snow.
when i tested my 4x4 out in the Jan snow this year, the tyres literally shovelled the snow out of the way, was really good...
thats my thoughts, probably wrong but hey, if you wanna stick bycycle wheels onto your trol then go ahead!