This map lets you see where ingredients can be found: http://srmap.uesp.net/
Use the "Show Resource" function at the top.
But just from playing the game a lot, I can suggest Canis root, Spiky grass pod, Nirnroot, and the red/blue/purple Mountain Flowers.
I think you can be a bit flexible though, especially at that specific location. Plants like Tundra Cotton, Nightshade, Thistle, and Lavender would probably feel natural there too.
You can find blue mountain flowers in snowy areas, like along the road just outside Winterhold, and near the Nightgate Inn. And I think I've also seen red and purple mountain flowers in snowy areas.
I wouldn't let cold weather deter my gardening. After all, one can find butterflies flying around near the snowy road at Stonehills. Skyrim is filled with hardy flora and fauna.
For sure.
And like I suggested, Heljarchen Manor's location is right beside the warmer climate of Whiterun. I don't think some of that flora in your garden would break immersion.