I did it last winter, and it almost killed the love of the sport for me.
It's not a sport, it's transportation. There is no need to love it, although I do love the convenience relative to driving my car.

the royal PITA of riding a bike in dirty road slush
Only a problem without fenders.

frozen toes
Lose the clipless and get boots and platforms.

and three hour commutes that should take only an hour in summer
That's what happens when you drive a car in rush hour around here. One of the good things about winter bike commutes is that snow and ice don't affect your travel time much. Maybe it's different in Colorado.
Do you have proper studded snow tires on the bike?

It's unfortunate that most of the bikes and bike gear sold in this country is geared toward recreational riding, but the more practical stuff is also available. Maybe the winter cycling forum would have some ideas for you.