No idea how to handle snow: in MD a couple of years ago, the governor took the snowplows off the roa

Mapquest tells me it would take about 30 hours of driving to get from Houlton, Maine to Miami. That assumes no traffic, and sounds about right to me. How many days that is, depends on how many hours you can stand to drive alone each day.
BTW, is this a round trip drive? I did a quick search and found you could fly from Fredericton to Miami on February 7, return on February 21, and pay a grand total of $593 (US). This would be comparable to the cost of gas and lodging for the three day drive each way. Not to mention wear and tear on your car -- and you! You'd have to rent a car (about $340 grand total for two weeks), but you may consider that worth the extra days in Miami.
I checked one more thing: fly from Boston-Logan to the Miami area and your total, and the round-trip cost goes down to $200. Add a $340 rental car plus $183 for two weeks of parking at Logan; and it's less than the $755 round-trip Amtrak auto-train -- without having to drive from Boston to south of DC.
Again, I'm just suggesting alternatives. My whole idea goes out the window if this is a permanent or long-term transfer, or if the OP has a large amount of stuff to transport, or if s/he just doesn't want to fly. I'm just noting that flying could be about the same cost as driving.
You need to allow two days each way for bad weather delays. South of Philadelphia/Wilmington, they have no idea how to handle snow, and they get a lot of ice which of course you can't do anything about at all. If you don't need them on the way down, fine, you can add them on to your holiday.
No idea how to handle snow: in MD a couple of years ago, the governor took the snowplows hotels in downtown san diego off the road because there were too many cars for them to work instead of closing the highways to cars until the plows could clear them. Duh.
I think there it depends on luck, your "driving personality" and where you're starting in Atlantic Canada as to how long it will take you . I've met people who said they drove from Montreal to Myrtle Beach, South Carolina in 16 hours doing it straight (taking breaks by switching drivers). Then there are my parents who drive close to the speed limit, take breaks, don't want to over-tire themselves and consequently take two days to go the much shorter distance from Montreal to Washington DC. Maybe not the best point of comparison, since Montreal is closer to DC than Atlantic hotels in downtown san diego Canada, but gives you an idea.
I think I would count on at least two overnight stops along the way and possibly at least three stops depending on your start point in Atlantic Canada. Best case scenario, if you're near the New Brunswick-Maine border, I'd say you're looking at getting to the Mid Atlantic States hotels in downtown san diego first day after some hard driving. If you drive hard again, maybe somewhere South Carolina, Georgia, hotels in downtown san diego northern Florida second night. Don't underestimate traffic in the Boston, New York, Philly, DC/Baltimore areas. Once it took me three hours to get from DC to Baltimore due to traffic delays and once four hours from DC to Richmond, although these are worst case scenarios.
Four hours from DC to Richmond (I-95 at the junction of 495 Beltway in Maryland to intersection of I-95 and I-64 in Richmond) is sadly not a worst case scenario. It is the new norm if you hit 495 after 3-3:30 PM.
Traffic is stop and go all the way to Quantico at best and to Fredericksburg at worst or more normally. Even worse in bad weather, though perhaps the completion of construction around hotels in downtown san diego Lee Bridge will help. Occoquan has become less of a bottleneck since they finished the major bridge work there, but the reintegration of traffic hotels in downtown san diego from the high speed lanes continues to cause backups.
If I had to do this trip, I would stop in Milford, CT or near there and get on the road toward the end of the NYC rush hour -- maybe 8:30 to 9. If you stop only for gas, it will take you about 6 hours to Fredericksburg, VA BEFORE the DC rush hour.