Fun fact: A nap should take 20 minutes. Not less, not more. That's because our sleep rythm goes in 20 minutes cycles. Maybe for you those are 18 or 22 minutes, but never 15 or 30. A 20 minute nap will leave you rested for the rest of the day.
when its cold and rainy outside, it feels so good
"I need a rest from my rest" - me.
sleeping on cold bed not a good idea,you body generate heat more and make you tired. the reason why you got morning wood.
probably because you tried to solve feeling tired by napping, instead of eating healthy, exercising, and sleeping enough at night in the first place.