As Steve has already mentioned many of the trails are likely snowbound. Your best bet may be in the Kootenay Plains area which is about 4 hrs drive from Edmonton if the roads are reasonable. I have not been there since last fall.
Generally speaking the area will be drier than the main ranges farther west. You will be also be assured of solitude this time of year. It is unlikely that you will be able to hike too far above the North Saskatchewan Valley floor without encountering snow. It may be possible to hike up a few ridgelines in the area , but these would be day hiking options not overnight trips. Subject to snow conditions you may be limited to walking in on flat terrain for no more than 3 hours.
The closest large town would be Rocky Mountain House , which is about two hours to the east along Highway 11. The small town of Nordegg (within 45 minutes of the Kootenay Plains does have a restaurant or two , a gas station , hostel and hotel.
A decent resource for trail descriptions is a book entitled David Thompson highway - A hiking guide. The book covers the area from Nordegg west to the Jasper Banff Highway. The area that I have described above is listed under the Kootenay Plains section.