Reconciling high ceilings with New England cold weather

Your heating system is sized for your house and climate. At some outside temperature, it will reach a point where ANY SYSTEM, running all the time, cannot input enough heat to compensate for the heat exiting via the roof, walls and windows.
The rate of heat flow equation is analogous to Ohms law I = V/R Take I a rate of heat loss, V as the Temperature difference on either side of the wall and R as the Thermal Resistance of the wall. The greater the temperature difference, the faster you lose heat. When you lose heat, the rate slows down and you reach an equilibrium.

A heating system able to maintain 65 degrees in the coldest weather you experience is probably adequate, but barely so.

Keep in mind that the ground itself also gets cold. In prolonged cold snaps, such as we've had this winter, it is not surprising that you have a cold floor. The ground might even have frozen underneath it. This is not expected behaviour in Florida.

The fact that you're using heat pumps also comes into play. We don't use them very much up here in Canada, because our winter temperatures are too low for them to work efficiently. A heat pump is trying to suck the heat out of the outside air and dump it in the house (like a refrigerator running backwards). The colder the outside temperature, the less efficient this is.

I assume you have a two piece split jamb pre-hung door. It's expected that these will be smaller than the rough opening, you need room to make the door plumb and level. Here's the install steps off the top of my head and my own personal best practice:

1. Check your width of the rough opening to ensure the trim will cover any gaps left, this is the main concern with the width. If the gap is over an inch, you can add a plywood filler strip to the side opposite of the hinges. A 3/4" to 1" gap is useful for adjusting plumb.
2. Check the plumb of the rough opening to determine if the door needs to sit on one side or another, and if it needs to be pulled out from the top. The first priority is to roughly identify where the top hinge needs to be to allow the rest of the door to remain plumb and level.
3. Separate the two parts of the door (along the split jamb) and set aside the half without the door attached.
4. Place the door in the rough opening, add shims to the top to make it level, and screw the top of the door into the header with trim head screws through the shims.
5. Check the hinge side of the jamb for plumb in both directions (side to side and in/out) with a long level or a plumb bob, add shims near the hinges where necessary (often installers will try to get the hinge side as tight to the rough framing as possible) and screw the jamb through the shims into the jack stud. You'll want a few screws near the top hinge for stability. Work from the top to the bottom of the hinge side of the door, double checking for plumb as you go.
6. Close the door, add shims until the gap between the door and jamb is even. You can double check for level, but the priority on this side is a consistent gap. You want to door to strike the stop at the same time on the top, middle, and bottom. Screw the jamb through the shims into the jack stud from top to bottom, double checking the gap between the door and jamb/stop as you go.
7. Cut off any shims that protrude past the finished wall surface.
8. Insert the second half of the split jamb. Finish nail through the stop to hold it in place, add a few trim head screws where your shims were located. This piece carries no load, so you don't need much.
9. Finish nail through the trim on both sides of the door to hold it tight to the wall surface.
10. Spackle, caulk, and paint.
11. Install door knob, strike plate, and any other hardware.