They don't have YOMD, but many of the TS we ate in march had the option of a cup, which was a few $ more than a regular drink.
At 50's PT, we got cups with capt. hook and tink on it, and a clip-on light up figure on it. They are a sturdy plastic, ith lids, and e use them on a regular basis, and they are dishwasher safe.
Another place, (i don't remember where, sorry!) we got a semi-clear plastic cup with Mickey on it, which came with a blinking ice cube.
The popcorn buckets (my favorite souvie) all are YOMD themed.