It is an entirely doable trip.
One just has to watch the weather, and have planned places to stop for such inclement weather should the need arise.
USMC46, the weather out here on the plains where I live has been terribly cold all winter long. However, seems the inter-mountain area of Livingston-Bozeman and Missoula areas has been warmer than out here on the plains.
Snow cover is not bad further south of me in the Nebraska and further south areas, so wind conditions should not affect your travel in those areas.
I suspect freezing rain conditions in the Oklahoma, north Texas and such areas would be the biggest concern, and I don't know the latest weather conditions in those areas now. So perhaps those roads are in good conditions and nothing to worry about in that regard.
Might I also advise you check on what in my parts is known as a winter survival kit to carry along for your vehicle. Blankets, candles, emergency gear. Heaven forbid that you will ever actually need it, but better prepared that not.
As before, this is an entirely do-able trip. Go for it and enjoy the ride.