Oil pressure gauge sluggish
A similar issue in the cold is a sluggish and/or very low oil pressure indication. It might be real or it might be slow response by the gage due to thick, cold oil inside that small diameter tube to the oil pressure gage.
Similar to Carl’s suggestion to use speedo cable lube for the tach drive cable so it will work better in the cold, fill the oil pressure sensing line with a light oil (I fill it with Marvel Mystery Oil) so that the gage can accurately and rapidly respond to oil pressure changes. That way you know for sure the indicated pressure is what the gage is actually trying to tell you rather than wondering if the number presented is really your oil pressure number or not.
I find the easiest way to fill the oil pressure sense line is to remove both ends and then gently blow the line clear with air pressure from the gage end of the line. Blow it into a rag to avoid making a mess in the engine compartment. Then have a helper in the cockpit with a rag held under the open gage end of the line. You start pumping thin oil into the line from the engine connection end (I use a pump style oil can loaded with the Marvel Mystery Oil) until your helper tells you that oil is coming out the gage end of the line, at which point the helper plugs their end of the line with a fingertip so that no air can get into the uphill end. This creates an airlock that holds the oil in the sensing line while you remove your pump oiler and connect the engine end of the line to the sensing port on the engine. Once the engine end of the line is attached to the sensing port your helper can now remove their finger tip from the oil line and get out of your way while you reconnect the uphill end of the sense line at the gage. Now your oil pressure gage will respond almost instantly to oil pressure changes and the presented number should be reliable regardless of temperature.
If any of the oil in the sense line should get into the crankcase oil it’s not a big deal because you used a thin oil that is compatible with the engine oil, right? However, there is no motion of the oil in the sense line because it is trapped in a dead end run of plumbing so it is unlikely to mingle into your engine oil. When removing a sense line years after filling it with MMO I find it still is pure MMO in the line, no indications of engine oil in the line that I can see.