I would also expect the new furnance to provide better heat than the old one. First thing to to is be sure you didn't arrange anything in the room different from last year. You don't have anything blocking the air registers. Check and make sure the air filter on the furnace is not clogged. If the room has only one register leave the door open so the colder air can circulate out of the room. If nothing in the room has changed contact the installer and ask them to check for any blockages or leaks that might be preventing the heat from reaching the room. It may be a problem with the blower pushing the air to that end of the house. If you have never had it done an energy audit is always a good idea. Most utilities offer them for free. They may point out missing duct insulation or air leaks that make the room colder than the rest.
Yes, the room can be very cold because of the floor.
Concrete slabs do not insulate well (R-value around 0.6!), and they lose most of their heat along the outside edge of the slab (the ground beneath the slab is a decent insulator). Using a Heat Loss Calculator, I assumed you had a 10x10 room with a completely uninsulated floor (concrete), uninsulated walls (stick built w/drywall), and ceiling (drywall ceiling with an uninsulated attic).
Heat loss was 4050 BTU/hour from the floor, 5440 BTU/hr from the walls, and only 1540 BTU/hr from the ceiling.
So, while your ceiling may be a factor, it's probably not the most major factor. Given that your floor is very cold, you probably don't have much (or any) insulation on that slab.
On the outside of the building, see if you can see the edges of the concrete slab. If you can, then it's not insulated. Buying some one-inch R-5 foam insulation and affixing that to the perimeter of the concrete slab drops the heat loss from 4050 BTU/hour in half to 2050 BTU/hour. Two-inch, R-11 insulation drops the heat loss to only 1050 BTU/hour.
Placing a rug on the floor would likely be insufficient, as carpet only gives an R-value of around 1.3 (and an area rug isn't going to cover the entire floor, anyway).
Edit with more information:
Consider a house built on an uninsulated concrete slab. Insulating the slab can lead to a reduction of 10-20% in total heating costs. Of the heat lost through a concrete slab, up to 80% is lost through the exposed outside edges.
Best Answer
Sounds like your concrete slab is un-insulated around the perimeter and/or the bottom. The very conductive flooring material (tile) doesn't help; the combination of these two means that the floor has very little thermal resistance to heat flow, so you constantly lose heat through the slab.
If the heat you generate is quickly rising through the second floor, it sounds like you have a secondary problem of too little attic insulation, which is causing the rising heat to rise right through the attic rather than get stuck at the second floor ceiling due to all the insulation that should be there.
The second problem is easy to fix: go up into the attic and air-seal all the places on the attic floor that are open to the living space using caulk and canned spray foam, and then blow 15" or more of cellulose onto the floor, covering up any existing insulation up there.
The problem with the slab is harder to fix. If you have bare dirt around your house rather than a concrete walkway, you can dig a trench around it to expose the perimeter and add rigid EPS or XPS foam insulation panels (not polyiso, it absorbs water). If you do this, take the time to add perimeter drains too; there'll never be a better time.
If that's not an option, and I assume you'd like to keep the tile flooring, you can always cover it up with rugs. It's surprisingly effective. Russians love their rugs.
Finally, it sounds like you have a poorly-designed heating system. Even in a badly-insulated house, heat isn't supposed to pool in the second floor like that. Old houses with ducted furnaces but lacking much insulation commonly had all the returns on the first floor to encourage air mixing. But without more details about your heating system, it's hard to say more.