I managed to change money at a bank in Zamyn Uud even though it was Christmas Day!
Nobody seems to have advertised exchange rates such as a handwritten or computerized sign. Since it was cold I just went in to the first bank and asked them if they could change tugrug to RMB. I did not shop around.
According to coinmill.com the official exchange rate was 1
CNY : 264.64
MNT. TDB bank on the square in front of the train station charged me 268.60, which cost me about $4 to change about $200.
After crossing the border into Erlian, China, I'm pretty sure I saw people entering and leaving some banks, which means they're also open on Christmas Day in China!
Again I have not seen any exchange rates in bank windows, nor have I seen any currency exchange places.
There is a covered public market mainly used by Mongolians here shopping for stuff to take back to Mongolia or to sell products made in Mongolia to people here in China.
A bunch of ladies hang around near some of the entrances and offer to change dollars but also change tugrug and RMB of course.
The initial rate was very bad so check the internet, make notes, and haggle!
I managed to change 61,320
MNT for 215
CNY, which means an exchange rate of 285.21 - worse than I got I got in Mongolia at the bank, but haggling was fun and it cost me less than $3.
The ladies told me the banks do not exchange tugrug and RMB but I suspect this is not true. Later I even found a bank inside the marketplace and though there were still no exchange rates posted I'd be pretty sure exchange was its main purpose for being there.
I'll also update the answer when I get to Hohhot, the capital of Inner Mongolia.