I know this is an old question, but I'm in a very similar situation to the OP's. I have bikes, an ElliptiGO, and a Catrike. I have done some winter biking, but I think the recumbent is much better suited for this, for a few reasons:
- You can go as slow as you have to, or even stop, without having
to disengage your feet from the pedals. If necessary, put it in a
very low gear and just spin.
- It's possible to tip the trike
cornering at high speed, but it's very difficult. It's not going to
slide out from under you on ice.
- If you put a studded snow tire
in the back (this is the "tadpole" (one drive wheel in back, two
steerable wheels in front), you can just lean back for more
As I mentioned, "tadpole" is one drive wheel in back, two wheels in front. The other style (two in back) is called "delta." Deltas are usually higher off the ground, but to have two drive wheels, you need a differential, which increases the price substantially.)
Just to comment on what others have said, you certainly can get front fenders and mud flaps for most trikes. You can even get fabric tops (e.g., Veltop) or velomobile shells for them.
If you're riding on roads, the width may be an issue, since trikes are wider than bikes. I'm mostly on bike paths, so it's not a problem. Of course, you can always just ride down the middle of the lane. That's legal and often preferred in the U.S.