Whether you're cooking in inclement weather by choice or necessity, the biggest key to success is a good attitude. Don't complain. Laugh. Make the adversity part of the fun. It's sure to be part of the story later.
Try to draw your guests or family members into the adventure. Share the bad weather under an umbrella or canopy or beside an open fire pit. Or solicit help in the challenge of figuring out ways to grill against the odds.
Don't let all your hard work go for naught: If you're grilling in rainy weather, use that umbrella to get the food quickly to the dry place where you'll be eating. If your problem is extreme cold, warm a platter ahead of time so that your perfectly grilled food doesn't chill while you're carrying it to the table.
If you're wet or the temperatures are frigid, substitute a hot drink for that tall cool one in your idealized image of grilling.
And always keep in mind that grilling is about more than just the food. It's also about the relaxation and the camaraderie. That's true whatever the season or the weather -- as long as you use your head.