Do we have to do anything with open enrollment?

It would depend on which state she lives in. At least two possibilities I can think of:
1. Our state has no such thing as "long term Medicaid;" beneficiaries have to fill out or review their eligibility form yearly. Your state might be different though. And either way, "nope," this has nothing to do with so-called "Medicare open enrollment."
2. However some state's Medicaid bureaucracy automatically and/or arbitrarily puts people on Medicaid in nursing homes in Medicare Part C and Part D plans. See if that applies in your mother's state and to your mother and -- if so -- if you think the plan the state Medicaid bureaucracy chose for your mother is the best choice in your opinion.

(I say "so-called Medicare open enrollment" because the time period October 15-December 7 applies only to Medicare Parts C and D and not all of Medicare. Also anyone receiving Social Security Extra Help/LIS can change Part C and Part D plans every month if he or she wants so the current time period doesn't really apply to them either. And people on a state pharmaceutical assistance program -- which not all states have -- can change Part C or Part D plans now and one other time during the year, so they are also less affected than the relatively small group that has to make a decision now.)

nope