That's another typical behaviour though - being all charming and funny, etc. for the professionals. They'll have seen it a million times before. They know the signs. His behaviour is so obvious, it's textbook - and he doesn't even know it.
He's doing everything in his power to get to you - and it's working.
Keep everything in writing. When you discuss holiday dates, add something like "If you haven't confirmed your contact by XX XX XXXX, I'll assume you aren't seeing DD at all during the [half-term/Easter/Summer] holidays and will make other plans." Keep it totally objective - talk about the facts. Give deadlines. No emotion.
When he contacts you at the last minute to say he's collecting DD, you can quote previous emails. "As per my email dated XX XX XXXX you didn't respond with your details of contact, therefore we have made other plans. Let me know by XX XX XXXX if you'd like contact during next school holidays - which start on XX XX and finish on XX XX."
Talk to the school. Arrange a meeting with the head and just go and have a chat. Tell them how hard things are - you won't be the first person to have a knob of an ex. Just say that of course you'd like things to be amicable for the sake of your DD, but unfortunately they aren't and you need to make them aware of the situation - they will see from a chat that you're reasonable and in no way 'erratic' or 'acting demented' - ask if they can they suggest anything regarding her homework?
I have no idea what to suggest about the coat, shoes, etc. Except perhaps walk her to school in a different coat that you then take home with you when you drop her off on Friday (or let the teachers know she has to leave it in school over the weekend and use the one at her dad's while she's there) - sorry, crap suggestion. I do think though, the less you rise to it, the less he'll do it. Easier said than done when it's snowing, I know. The fucker.