I doubt that. Average January temperature for Denver (5280 feet) are 32F. Average January temperatures for Mt Rainer (assuming that the measure is at Paradise Valley also at around 5000 feet) is 29 F. Average January temperatures in Frisco, CO (9000 ft) is 17 F. Leadville (10500 feet) is also 17F. On the other hand, the record low temperature for Denver is -21F, Frisco is -41F and Leadville is -27 F. Paradise Valley's record low? -13F. Sure it might get colder higher up but the Pacific Northwest has the Pacific...a giant heat reservior...to the west that mitigates the temperatures somewhat. The Colorado mountains don't have that reservior and they tend to be on the recieving end of a river of cold air from Canada.

Temperature decreases pretty predictably with altitude. The temperature at 14000 feet undergoes some slight variations but the top of Rainer is going to be about the same temperature as Mt Evans if the conditions are similar. You aren't going to be able to climb Mt Evans in the dead of winter in shorts. They have similar clothing requirements for similar times of year.