At anytime, the minimal amount of lube that's necessary for the gun to function is the way to go. There isn't a single thing on any bolt action gun that needs grease on it, other than a VERY VERY light smear on the back of the locking lugs and a tiny bit on the back of the bolt assembly where the cocking cam engages. Everything else should have a VERY VERY light touch of oil, and only if it's needed.
When the temp is going to be below 40 degrees, I strip all of the lube of the gun with brake or parts cleaner. When it's going to be cold, it's best to run the gun dry or to use graphite dry lube (powder) VERY sparingly, as it doesn't freeze. There are some of the new synthetic lubes that can be used in the cold, but I don't use them myself.
There are MANY more problems caused by over-lubricating a firearm than were ever caused by one not having enough lube on it.