Plugged in long term

As others have said. Depends on the converter.

Progressive Dynamics Intella power wizard jobs.. You bet Great idea (I just put a new 9180 with wizard in my RV since the teenager that was in it rebelled. er, failed.)
(Just. like 10 amp today).

Magnetek 6300... Bad idea.

Others... Depends on the converter.

One of my silly over-the-top items.

Apply some silicone dielectric grease to the blades on the plug before inserting it into your building outlet. Some how SECURE the plug to the outlet ! Spit, glue, bubble gum, tie wraps, twine, even insulated solid wire, whatever it takes !

I always wished that the TT industry had gone to twist locks, but they are not perfect either !

not a problem. worry more about frozen pipes.

A battery charged to 85% won't freeze until about -62 degrees F per Trojan...http://www.trojanbattery.com/pdf/WP_DeepCycleBatteryStorage_0512.pdf

I leave the batteries in, just plug in the MH for a day or 2 every 3 weeks or so and turn the batteries off in between after confirming that they are fully charged.

If the batteries are charged and disconnected, they also won't freeze over the winter (and won't self-discharge very much as the rate of self-discharge is heavily dependent on their temperature).

There's no problem with leaving the charger going, either, if it's a multi-stage charger. If it's not, it may be well to put it on a timer and have it run perhaps an hour a day or so (and, of course, also keep an eye on the electrolyte level in the batteries). It can be very nice indeed having power available in the RV if you have need of checking or doing anything in it.

For dozens of years we have left the RV plugged in and as long as batteries have fluid they live well.

If your rig has smart converter then I don't see any downside on keeping the rig plugged in during winter. If you buy an inexpensive Trik L Start this device (easy to install) will maintain your chassis battery whenever your plugged in - good investment.

I would think that would keep the batteries charged, but with winter temps in your area in double digit negative numbers, I'm thinking you should still winterize your plumbing system.

Winterizing class A