I'd Replace all air, and fuel lines, hoses, filters, plugs and wires too. Of course you'll check the function with each new hose, belt, whatever. Along with new gas, I'd add some fuel stabilizer. I use it year round, because its cheap enough. Specific radiator hoses are typically a bit pricey, so those can wait...for now. Your okay plowing the yard if a hose breaks. But if you ever take it on the trails, then I'd replace those hoses as soon as possible after this other issue gets solved.
What you're likely dealing with, is a combination of things. Most, if not all, from the sound of it, are from lack of proper periodic maintenance. I'd do this first, since it needs to be done anyway.
Besides, you might get lucky, and find the problem while you're doing this.