Wrinklers have no effect whatsoever on how many cookies you get from reindeer, nor do the reindeer have any effect on how many cookies wrinklers suck.
How many cookies you get from reindeer depends on three factors:
- Your cookies per second (CPS). It will give you exactly 60 seconds worth of production
- This is related to 1. If you have any frenzies active (Clot x0.5, Frenzy x7 or Elder Frenzy x666) you will get the multiplier tacked on as well.
- If you have the "Ho ho ho-flavored frosting" upgrade, you will get twice as many cookies
This means a reindeer will give you 1/10th of the cookies a 'Lucky' golden cookie gives you, but with the benefit of not needing a large enough bank to receive your maximum prize.
Wrinklers will decrease your CPS by 5% each and give back extra cookies when popped. Due to a stacking effect the more wrinklers you have on the screen, the more your CPS increases. Having 10 wrinklers on the screen essentially results in a 6x CPS boost.
Note wrinklers also stack with frenzies. An Elder Frenzy (x666) with 10 wrinklers on is equivalent to 666 * 6 * 12 seconds = 13.3 hours worth of cookie production!