I used a dual-purpose XL-250 with enduro tires with sheet metal screws in each knob. Worked well, but was totally illegal. You might be able to stud a knobby or enduro tire. I think a street bike would not work nearly as well - wrong tires, and I needed flat track style cornering, which would be harder on a pure streetbike.
Try the 360 as-is with good street tires. It doesn't take long to get the hang of riding in snow or slush - practice on no-traffic back roads until you get the hang of it. Wear good protective gear and explore the limits of the bike with the usual avoidance maneuvers. You'll crash a coupla' times, but it will be at reasonably slow speeds and sliding on snow doesn't hurt you or the bike that much. And your 30-year-old bike limits the downside on your wallet.
Fresh ice is a problem. It's almost impossible to negotiate slick ice in traffic on a street-legal machine - plan on cooling your heels in a Tim Hortons until the sand truck goes by. Also, watch out for those nice, sunny winter days when the roads dry up everywhere except where there's shade. You'll be amazed how little you can do when you hit a 100 yard stretch of glare ice in the shade of a fence row of pine trees.
All that said, the deal-breaker for riding on or during frozen precipitation is traffic. You can never stop at an intersection without worrying about some jerk in a cage losing traction and rear-ending you. Even if you see it coming you may not be able to find enough traction to get out of the way quick enough. Best bet is to buy a "winter beater" cage for the days when the roads are covered with the white stuff, and save the 360 for the sunny ones.
I've got caught out a few times, the last time was coming home from work on my Trophy. I made it to within a mile or so of my house when a city bus lost it in a corner and slide past throwing 1/2 a ton of slush in my lap, couldn't see sh*t plus my bike gained about 100lbs of weight on the windshield and me.
We hit snow at the top of the pass the other day but the roads were just wet. If you're seriously thinking of riding in snow on the street, make sure your insurance and medical coverage is up to date, you'll probably need them.
I rode from Ely-Eureka-Carlin-Elko NV on my PD on a memorable Mother's Day a few years ago, slush and snow all the way. What made it tolerable was that I saw only three other vehicles the entire way. It is surprising how well a motorcycle can go in such conditions if you haven't tried it. But - It is nuts enough to share a snow or ice covered road in a car in traffic with all the incompetent idiots out there. The only real self-defense you have on a bike when somebody does something stupid is whatever you can do with the traction you have, whether it is braking, swerving, or accelerating. To ride a motorcycle on a snowy or icy road with traffic strikes me as the height of foolishness. But maybe it is different in Canada.
Unless youre a masochist, dont bother. Ive ridden in snow, fallen over and been unable to get off the bike because I was frozen stiff,and gone arse over on black ice. One time I was trapped against the kerb when a semi trailer slid down the iced up camber of the road. Even if you manage to stay upright, its no fun watching the other vehicles sliding towards you. Plus ,bones break real easy in freezing temperatures.
I used to ride all winter in the snow 100 miles south of Chicago. I would wrap short pieces of 1/8" cable in a figure 8 pattern around the tires and spokes of my R75 BMWfor traction. It worked great. I would run a TeraPlane sidecar sometimes. Sidecars are the most fun in the snow because you can steer with acceleration or deacceleration as well as with the handlebars.
I got caught riding in snow all the way out of Yellowstone this September (From Grant Village out the East entrance/Exit) It took about 4 hours and was a mix of snow, slush, mud and slush/mud/water filled pot-holes for quite a few miles. They are completely rebuilding that entrance and most stretches no longer had pavement (or guard rails). I thought I was home free after that only to get caught in the Bighorns with even more snow. Had to deal with 2" of accumulation on the road and it was coming down so heavy that I had to keep swiping my face sheild about every 10 seconds just to see the road. I found that if I drove about 20 mph I wouldn't have to lean the bike over in the curves and as long as I didn't use the brakes or try to accelerate I was fine. I actually never did use the brakes until I got out of the snow.
I was extremely glad to be on my DR650 with new tires more orientated to off road riding when I got caught in all that crap.
I agree with longride and sarnali about the insurance and would add a good life insurance policy if you are married or have kids.
Time for some "real" advice.....do it but prepare. Get a Bruno Wessel stud gun, put in the carbide street legal studs on your enduro tires...no street bikes please. My Valk stays parked when there's ice around. Use a dual sport/enduro bike and gear up properly...get electric stuff if needed. Go ride, slide, & practice. Join the ranks of the truely insane, wear your carbide studs with honor, and still save money on gas!!!
Anyone try attaching, or have seen someone else attach, a ski to the front of a modern trike or sidecar rig? I saw an old photo of a harley sidecar rig with chains on the rear tire and a ski up front... Looked doable to me...