I would halve the squash and remove the seeds, then slice it thickly and brush with olive oil. Maybe marinate the slices for a couple of hours. then dry the slices off and season with salt, pepper and herbs (I love dried herbes de Provence). Grill on indirect heat. It will take a while because the squash is raw, but not all that long for slices. Grilled slices are really delicious. You might like to make an aioli to serve with the slices.
Since I think all of those previous suggestions are great, I'm just going to say what's really on my mind: There is a foot of snow where I am (Canada, of course) therefore you are a meanie pants and should send us some of your nice weather.
Well let me tell you...if you could send me snow, I'd love it! I've a ski house and snowmobiles about 2 hrs from my home in Pittsburgh, and last year snowmobiled for an hour and a half. Did not get to ski once. So maybe we can barter! Haha.
I would imagine one thing you could do is peel and slice the squash into 1/2-inch thick slices that are long and wide enough not to fall through the grill, toss them with olive oil, salt, and pepper, and grill them as you would summer squash slices. Unless you have one of those hubbards that is so hard and huge it's halfway impossible to slice it up. I wonder if you could cook the whole squash in a covered grill until it's tender like you would a large cut of meat (like a turkey!)
The method in this video is great and could easily work on a gas grill (charcoal too, with a little more attention to keep the coals going.) You could also cut the squash into wedges to cook faster. http://www.food52.com/blog/2695_how_to_roast_any_winter_squash
You can par-boil your (peeled, sliced) squash and then grill it on medium to minimize the grilling time. Before putting them on the grill, brush them with olive oil, salt, and whatever other seasonings you'd like!
Also, here's a great grilling recipe for summer squash: http://www.food52.com/recipes/265_tuscan_grilled_zucchini_summer_squash
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Also, here's a great grilling recipe for summer squash: http://www.food52.com/recipes/265_tuscan_grilled_zucchini_summer_squash