Comparing training and validation data set Root MSE for a best subset regression?
Im a little late, but better late than never.  It looks like your line where you find the coefficients: 

regfit.exh=regsubsets(HPV~. -Model.Types..code.-Year..code.,data=Mydata, nvmax=NULL,force.in = NULL, force.out = NULL, method="exhaustive")


should have data=Mydata[train,] instead of data=Mydata.

Your model had already seen your test samples, so the validation error is not an accurate assessment.