There are many good options in MN for protecting a home from N.H. I'd like to specifically point out that MN doesn't allow any trust (revocable or irrevocable) to protect a home as suggested by other answers. MN also doesn't allow a home to be considered an unavailable asset unless you or a spouse are living there at the time of application (unlike some states that allow an exempt homestead). These laws are different from state to state. I recommend consulting with an Elder Law attorney as soon as possible to give yourself the most options. Best wishes.
There are a few strategies available that may solve your problem. In many states, a disabled child can receive the home during your lifetime without endangering your ability to receive Medicaid benefits. If that option isn't available and you have plenty of time before you need skilled nursing care, you may be able to protect the home using a type of trust. But the first step is to visit a qualified Elder Law attorney who can begin to answer your questions. In Minneapolis, I would suggest visiting Jeff Molever of the Molever Law Firm.
I am not licensed in your state. Your primary residence may be exempt from being counted as part of your Medicaid estate should you need skilled nursing benefits. Thus, you may very well be able to retain it and still qualify, however, the state will almost certainly go after it after your death if you have not done Medicaid planning. Since your son has MS and may be receiving government benefits, you really need to consult with a reputable elder law attorney who is experienced in Medicaid planning. You can search for elder law attorneys in your state by visiting the website of the National Academy of Elder Law Attorneys at www.naela.org.