Would an airliner be allowed to take off in snow?
Don't worry about it
While snow can sometimes cause a delay, airports are really good at snow removal.  (Especially airports like Denver that are used to getting a lot of snow.)
According to flydenver.com DIA has 500 trained snow removal people and 270 pieces of equipment to clear 12.2 million square feet of runway, taxiways, etc.
To put that in perspective, a typical highway (2 lanes each way, with shoulders) is around 38 feet wide each way, or 76 feet for both directions.  If I've done the math correctly, 12.2 million square feet is about 30 miles of road.
The state of Minnesota knows a thing or two about plowing snow.  They use about 1500 drivers and 839 plows to handle 12,000 miles of road.  To plow snow the way the Denver airport does it, they would need 200,000 drivers and 108,000 plows.
Here's a YouTube link that shows off some of Denver's bigger snow removal tools.
Chances are, if you can get to the airport you'll be able to fly (but perhaps not on time)