A brand new mobile home was put on 4 acres that I own and there is another much older mobile home on the property, which one should carry "Homeowners insurance?
Talk to your insurance agent. You at least want liability insurance for the whole property. If there is a loan against either of the mobiles, the bank will insist you insure it; ask them what their requirements are.
If there's no loan, And no local legal requirement -- which the agent should be able to tell you -- this becomes like the question of whether you need comprehensive insurance on a car. Do you care if a disaster destroys it completely or do you want some protection against that? Price it both ways; you may find that leaving one "naked" doesn't save as much as you expect.