We noticed the sign stating that there was a $19 charge for parking but it was waived. I would certainly ask about the parking when you are checking in. They seem to be very flexible about it.
I was able to get it waived with my Hilton Gold card. I never hesitate to ask to have parking waived.
We were surprising charged $19/day and politely talked them down.
There was when we were there in Jan 17.
Get an answer from Hilton Santa Fe Historic Plaza staff and past guests.