It would be fun to try one but I think it might create as many problems as it solves.
- Where do you park it?
- How fun is it to haul all that extra aluminum + canopy up a hill?
- How's the ventilation?
- Windshield wipers/defogger?
For a fraction of the cost you could get some really nice foul and cold weather gear that can come in handy off the bike too. I have a set of packable rainproof pants and jacket that I throw in the messenger bag when there's a possibility of rain. If it's going to be warm anyway, on the way home I might just say f**k it and just get wet. Who cares? As for the way in, just leave a towel at work and bring some extra clothes on those mornings when it's raining. Even with the rain gear I get damp. I leave my work shoes at work so that's a non-issue.
Dealing with cold is a matter of dressing in layers: Wicking base layer (long underwear), warm thermal layer (like a fleece pullover), wind proof outer layer (shell). I'm more comfortable with less clothes riding a bike in the winter than I would be in a car.
Riding in bad weather is 50% clothing+gear and 50% attitude.