Fear makes cowards of us all. Realizing that it is a mental game is a good start. It doesn't help that many players like to trash talk while you putt; I find that I have better scores when I play alone or with my gf (which of course doesn't matter if there's no witness).
I try to putt as soon as I can. Pausing, gives me a chance to think, which will cause me to miss more so than rushing the putt.
I've kinda gone to the Larry Bird philosophy. He used to go into the gym an hour or more before the game to shoot baskets, thus, giving him the mental edge over his opponents (or himself). I used to do the same with my jump shot when I played basketball and have recently started applying it with putting though I only need a max of 30 min to get the feel I need.
As far as adjustments for wind and such, I normally know that before I even pick up my disc and lay down my mini, so I'm ready to set my feet and throw. In closing, putting becomes second nature with much practice, but if you think instead of allowing muscle memory to take over for you, adversity results.