Dress appropriately. Bermuda shorts, Hawaiian shirt, flip-flops, and umbrella hat may be fine for August, but in February it's more than a fashion faux pas. By the time your burgers are done, you'll feel like your femurs froze.
Once you have a good, heavy coat, pants, boots and gloves on, remember: if you can't feel cold through your clothes, you can't feel heat either. Be careful how close you get to the grill, so you don't become griller flambé.
I don't recommend grilling in whiteout conditions, but wind doesn't need to be a big problem. A well-placed saucer sled, either held by an obliging family member or stuck in a convenient snowbank, often provides enough protection to not only light a match, but keep the grill's fire from being blown out.
A word of caution, though: particularly if you are using a snowbank to secure the saucer sled. Make sure that the sled is held firmly in place, so that it does not become airborne in a gust. Especially while grilling, you don't want to be hit by a flying saucer!
Allow more time for your meat to get done. Grilling times will increase when frostbite replaces heatstroke as a weather-related health risk.
Finally: have fun!