You have the same rights as everyone else. Where you're most likely to have a problem is whether your landlord will consider your possession and use "criminal activity" for purposes of the MHLTA. Washington's Medicual Use of Marijuana Act will likely protect you from a claim based Washington criminal law but it may not protect you from a claim that you are violating federal criminal law. It may also be a rule violation for the park in general. Short answer: use on rental property at your own risk. Your health care documentation may not be an effective shield from eviction. You might consider being up front with your intentions to avoid any problems in the future.
I agree with the previous poster, this is an issue that could go either way at this point. While you are most likely protected from state law criminal violations, it is still a violation of federal law. California had a similar issue revolving around a man being fired for using medical marijuana and whether his employer had to provide a reasonable accommodation under the ADA for his disability. The California court held that because marijuana was illegal under federal law, such an accommodation would not be reasonable. Washington is of course an entirely different state with separate courts and case law. The facts could be distinguished considering that an employee who is getting high at work is different from a tenant getting high at home. An employee can cause damage to a company, a tenant will probably not cause any damage to the property.
Like the previous poster stated, do this at your own risk. Whether it is legal or illegal or whether it would qualify as a reasonable accommodation is yet to be determined,
I would just like to add a few items to my previous answer. The court has ruled that a Public Housing Authority does not have to reasonably accommodate medical marijuana users in Assenberg v. Anacortes Housing Authority. Furthermore the courts have hinted at the idea that the MUMA only creates a right against criminal prosecution for state crimes and does not include federal prosecution. A recent Washington case held that in employment situations the MUMA did not create a duty upon employers to reasonably accommodate medical marijuana (this case may be appealed). The same reasoning could be used by a landlord in so far as it would not create a duty to accommodate the use of a drug that is illegal under federal law.