I do DC pick-ups every day and a few times over the last couple of weeks, DD has been whining/crying when we go to leave. She's fine when she sees me - smiles at me and reaches for me to pick her up but then when she's in my arms she scrunches up her face and starts reaching for DCP.

She fusses when I put on her coat and when I put her in the car seat she full out starts crying. She'll fuss on the way home (5 min. drive) but is all smiles when I get her out of the car. So weird. I know this has been posted before, but I always hear it happening when they're a little older and are playing with their friends. I know she has fun there and she LOVES DCP. Like, really loves her. This is a small in-home, and the woman who runs it is very attached to DD. She carries her around a lot, so I'm sure she's like a second mother to DD. But it still broke my heart a little when she cried when I was holding her. *sigh*. OK, pity party over.
Re: I didn't think this would start so early
I am dreading the day when this happens - so I do drop-offs
This is probably a little bit like bribery, but maybe when you pick her up you can bring a favorite toy or something new, cool, and distracting for her to help while you get her coat on and get her into the car.
I also found that DS will get upset if we switch from one of us holding him to the other one - even if he reaches for the other person he seems to regret switching arms after he does it, lol. It's an easier transition if one of us puts him down and plays with something, even for a couple seconds, and the other one picks him up. Strange, but it works!
DS really hates getting his coat on and this morning cried for me while putting him in the car seat this morning so I feel for you!
ETA: since your car is warm already maybe you don't even need to put a coat on her, just grab a blanket for the short time when you're outside if it's really cold?
Ditto this. Also it is probably a phase like everything else. We go through crying at drop offs right now which also sucks. She could just be disliking change so like pp maybe just a blanket in the car instead of trying to put the coat on. If she is fine once you get home just try and get to that point as quickly (and safely, not saying to speed) as possible - if comforting her in between doesn;t work just try to get on to the next thing quickly is what we do around here.