The path up to Summit Park from the tubing hill? I'd say that's a decent climb. Or do you mean something else?
A typical ride for us is to go from Jeremy to the Fieldhouse - about 8.5 miles round trip, pretty flat (maybe a total of 100 feet of elevation gain/loss each way?) and paved. That trip (honking cargo bike with 60 psi 2" slicks, 100 pounds of kid and trailer) kills the battery almost completely at mid/high assist levels (500w of assist) in the winter. If there's even a little bit of snow on the path, we bring the charger with us and recharge at the field house to make sure we get home.
In the summer the range extends out to Matt Knoop park/Silver Springs area which is another 4-5 miles of riding round trip. So the temps and rolling resistance make a HUGE difference.
I hesitate to guess what your range would be on some random Haibike fatbike. Obviously you don't have the extra weight to contend with, but you're 1) on snow/low pressure fat tires, 2) in even colder conditions a lot of the time, and 3) climbing big hills quite a bit (though I don't know what sort of approaches you're doing, just assuming it's uphill like most).
On the plus side, though, you can probably coast back down. You just need the battery to get you up there.
I'd say try it and see. Worst case scenario you have to buy another battery to carry.