Your tractor should be fine, provided the dealer put in sufficient anti-freeze in the radiator solution (easy to check). It's going to take a few more seconds for the glow plugs to heat up, but that's it. The battery when new will be fine for quite awhile, but there ain't no magic about batteries, tractor, boat, auto or otherwise, and with time the ability to maintain a full charge for a month at low ambient temperatures will diminish. My Kubota battery died last year (at 9 years) during the winter, and for the prior few years had benefited from a trickle charger when I wasn't using it every week or 2.