So I recently did a field strip and clean on my buddy's AR-15. It was so gummy it wasn't cycling, so I offered to give it a quick field strip to put her back in action, but would go no further as I didn't have a proper table with containers to go any deeper.
I've always had the same cleaning protocol.
1. Dry brush to remove any loose residue.
2. Apply solvent and use stiff bristled plastic brush - really like the dollar store stiff toothbrushes for this.
3. Use WD-40 to flush away solvent and wipe down parts. Finish with an air-dry, which with WD-40, only takes 2 minutes or so.
4. Apply a light coating of oil (hoppe's, Shooter's Lube, whatever is your preference) to wear surfaces or other points of contact. Use Q-tips for precise control and getting the oil into grooves.
5. Re-assemble and function test.
To the OP - if it's gummy, it's not lubricating your gun. If it feels tacky, that's the cold and you need something thinner, although it will probably be too thin by the time you put a mag or two through and some heat gets in the gun. I would first check to see if you might be going overboard with the lube to begin with.