The Under Armour tights would help, the class of Cold Gear they are would determine how cool it could help you be comfortable in. I use one of the Under Armour Cold Gear compression tops when it is cold enough here, keeps me very comfortable. I am used to standard Lycra shorts with a chamois in them so I don't try the tights from Under Armour, I have a pair of bib tights and a pair of outer tights from Nashbar for over my riding shorts. Having the tights over under wear and shorts over the tights would give several layers to have bunched up material that could chafe you, though. I'd say to look at some of the cycling specific tights and bib tights available, you can find some effective, comfortable ones without spending a fortune if that is an issue. Nashbar, REI, Ribble, Wiggle, and other on line shops have some bargains available. If money isn't an issue then the sky is the limit for good high end tights. Assos, Rapha, Castelli, Gore Tex, etc. all have excellent cold weather gear. Best of luck on your cold weather riding. I barely broke stride last winter, just a little planning was all it took.
Bill
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Semper Fi, USMC, 1975-1977
I Can Do All Things Through Him, Who Gives Me Strength. Philippians 4:13