Verbal agreements in any real estate transaction, whether a rental or purchase, mean absolutely nothing. If it wasn't written down it never happened.
Usually leases prohibit activities rather than permit them. What exactly does your lease state about animals and/or pets?
Given the length of time you've lived at the complex you're likely on a month-to-month lease so your landlord can also do the following to get you out even if your snake is a designated ESA:
- Require a new lease with a "no snakes" clause starting as of a future date, and if you don't sign it then you will receive an official termination of your current lease with a notice to vacate (30-60 days) before they start eviction proceedings.
- Require a pet deposit.
- Jack up your rent.
Personally I'd start packing.