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Sounds like an oil viscosity problem . Try running synthetic oil . There is an underlying reason for this , but without some testing we can only guess, this may help for now ...
Any chance it has to do with TPS? When my TPS was going bad you could put the pedal to the floor with no response, sometimes it would engage and go great. I would say it was intermittent. Doorman makes a replacement for about $50.00 at napa.
In the cold, if your batteries are not up to par, your truck will not start. Look at the date on your batteries. If they are a few years old, take them by a parts store and have them checked. If one is bad, replace both. That may be your "No start" problem, assuming your truck is cranking.
Before you replace, any national parts store will check them for you for free and tell you if they're bad. If only one is bad, replace both. Good luck!