Is this new behavior, or is it a new-to-you truck that you're driving in cold weather for the first time?
If it's a change from previous cold weather, that would suggest a problem.
My first thought is that you need to read the temperatures with a scan gauge, or on the dash readout if the truck has that option. The gauge is probably not exactly accurate.
I thought my 2001 Silverado had a "real" gauge rather than a buffered one because the reading would change with different conditions. I learned otherwise when it got hot in the school pickup line one day. Next time, I brought along an old tablet with Torque Pro to read the actual temps. I drew the image below as I crept through the line. Black is the gauge, and red is the actual reading from Torque.
My drawing is a little inaccurate--the gauge actually has three small marks between the larger, labeled ones. Reading left from the middle/210, (assuming the actual three small marks) normal range is from the middle mark to between the third one and 210. Temperatures and the general locations on the drawing are accurate. That shows just how off the gauge is.
If it does need a thermostat, I would recommend getting the GM Original Equipment model, from a dealer or someplace like RockAuto.