I'm not a heavyweight, but ride often with a fully loaded bike and a daughter on a Piccolo trailercycle, so my rear wheel has often endured quite a load. I rode my touring bike with 700x32 tires a lot, but preferred 700x37 on the rear wheel for loaded self-contained touring with my daughter in tow. Tire size is as much related to road condition than it is to the weight carried, and I'm aware that some heavy riders ride their tandems with 700x23 or 25... except they ride on smooth Georgia roads, not on pothole-infested Montréal streets and highways.
So should you have the tires swapped? I think it depends mostly on how good your roads are. You will increase your comfort, but at the expanse of (a little) speed. If you weigh more than 250 lb, the most important factor to check is wheel built. A good store should even out spoke tension, and if they offer you a "free tune-up after 30 days", ride heavily in the first month and notice if your wheels are out of true.
Winter ? I commute year round in Montréal; usually with knobbies rather than studded tires, because I deal with snow, slush and dry pavement, not bare ice. I use the studded tires only when we have a long period under -20 to -25 C, when de-icing salts don't work (and then, they don't sand either). Knobbies are available in 700x37 and (sometimes) in 700x32. For studded tires, the only one really worth consideration is the Nokian Hakkapelliita (see
http://peterwhitecycles.com), available in 700x37 and 700x45. For on-street riding, you don't need anything wider. It's for people who ride on packed
trails that 2" wide tires are useful.
As for winter riding, make sure your bike can handle fenders with the above tires.
Fenders with a mudflap on the front fender (see
here are not only great to keep your feet dry, but they also help a lot to keep your drivetrain clear of road grime, which is a worst problem in Winter than in Summer.
Xtracycle in Winter?
I don't have one and I'm not fond of the concept, except maybe for short distances. But I ride a touring bike and a tandem which have fairly similar behaviours (which means they
don't have the same front-end geometry), and I ride the tandem either with my 9-year-old dauther or by myself, so I am used to little weight on the rear wheel.
And that's indeed where lies the problem. The Xtracycle puts your rear wheel back by 40 cm (much less than on a tandem, where it is back by some 75 cm), so instead of having a 40/60 weight split (front/rear), the Xtracycle has a 60/40 weight split (front-rear). So if you ride on ice – especially without a rear studded tire – , climb hills with a very smooth rythm or your rear tire will skid. And don't brake too hard... for the same reason.
Another option if you don't plan to carry large loads often.
Why not bicycle and panniers? Then check garage sales or university sales for a used children trailer. That way, you keep your bike lightweight and nimble most of the time, and add a trailer when you really need it.