I don't know about everyone else's, but yes, mine is like that. I ALWAYS let my oil and coolant temp get above 100* before I ever put it in drive. But at 100* EOT and ECT, the tranny is not yet warm, so it does shift slowly and kind of long. But then again, I am always easy on the throttle till my ECT and EOT is above 160* which usually doesn't take too long.
Normally once my TFT is above 100* she will start to shift a bit more normal. I'm in N. Texas but in the mornings it's been in the low 30*'s recently and it will do it every day.
Edit: Oh and yes, on first crank when it is below 40* it will buck for just a second then it will run normal and not rough. Also not sure what oil you are using, but read the thread about the T5. It will help tremendously with the cold starts. With regular dino 15-40 she will run rough for about 5-10 seconds after starting, but the T5 helps tremendously with that.