I want to install a geo-thermal heating system, can I refinance my home loan. I have had it for 4 months,?

Yes, but unless you have substantial equity you may not be able to cash out. Try a home equity loan instead.

there is no law; financing has to do with what a lender will do; most require 6 mo ownership; dumb rule by any bank!

Refinancing doesn't depend on the age of your loan - it depends on the equity you have in your house.