Transmission slipping when cold, fine once warm, what is going on?

[phineasfogg]

Noticed over the last few weeks that my automatic feels like it's slipping slightly when I first start driving in the morning, the revs climb a bit before it engages and there's a delay going from reverse to drive. Once the car is warm after five or ten minutes everything is completely normal, shifts are crisp and there's no slipping at all. I've checked the fluid level and it looks okay on the dipstick, colour is a bit darker than I'd like but not burnt or gritty. A friend told me this is a classic sign of low fluid pressure when cold or possibly worn seals inside the box, but he's not a mechanic so I'm taking that with a grain of salt. I found a helpful resource on why an automatic car will not shift gears while trying to understand whether this is early warning or normal behaviour for an older transmission, and it mentioned temperature related issues which matches what I'm seeing. My questions are whether cold slipping is something that can be fixed with a fluid and filter change, or if it means internal wear that's only going to get worse. Also is it doing damage every time I drive it cold like this, and should I be warming the car up longer before moving?