if there's still a Sun 'n' Ski on Westheimer, they're the store with the most knowledgeable staff. That said, it's going to be be hard finding winter gloves/mitts in Houston that are what would be considered winter weight in Colorado.
Here's a radical idea for you. What about Eldora Mountain Resort just outside of Boulder. The bus from DIA to Boulder cost $10.00 per person each way, the bus leaves from Boulder going to Eldora around 8am each day, cost $3.75 each way. Eldora is at about 9,500 ft, with Boulder at 5,400; it's much easier coming from sea level to deal with altitude by playing high and sleeping low (just what climbers do when climbing Everest). There is both a Holiday Inn and Holiday Inn Express in Boulder. It's a small city of around 100,000 with an infinite variety of places to eat and be entertained.
Eldora has rental bibs (pants) and parkas in the rental shop. You will need your own long underwear (I'd suggest going to Academy - get a synthetic material, such as polypro - NOT cotton); mittens/gloves, a hat, and sunglasses or goggles (you will need one of the two to avoid snow blindness). If you prefer an helmet, those can also be rented.
I can find no outerwear rentals from the websites in the Summit County ski area, Vail says they have a limited
amount, but they will be glad to help you buy the proper clothing.
If you have any questions about Eldora, please feel free to PM me as I teach there.
[edit to add]
Eldora's first timer package (includes an all-day lesson, rental equipment, and beginner area lift ticket) is $87. Complete outerwear rental (bibs and parka) is $29. Website for Eldora