Try to avoid soap that dries or tightens the skin, especially around your mouth. I know my skin can feel tight after a shower because of the soap, and the trumpet is uncomfortable.
For morning playing, start slow. I'd suggest something like Stamp 3 (although I would stop at low F# and not play pedals when your chops feel bad). Play for a couple minutes and put it down. Come back a little later, and do more of whatever your normal routing is. The worst thing when you feel bad is to keep playing and playing and playing trying to warm up. Play a little, put it down (even if you still sound bad!) and come back a little latter. Eventually you'll adjust and you won't have to ease in like that.
Other things that help me are, avoiding salty foods, being physically active before I play, and doing something to attempt to start my brain too. I used to play Tetris for a few minutes and then walk around the music building for a little while. It seemed to help engage the mind and body. Good Luck!