"Hardy" refers to a plant's ability to over-winter, in the ground, with no protection.
The United States is divided into agricultural hardiness zones, and many plants are identified by their hardiness. For instance, if you look at a catalog it might have a comment that the plant is "hardy in zones 7-5. That would tell you that if you live in those zones the plant will go dormant over winter but regrow in the spring. In zone 4 you could probably get away with leaving it be if you mulched it heavily or otherwise protected it.
I don't know a single herb that cannot be grown successfully under lights. All you need is regular flourescent bulbs. The trick is to keep them only a couple of inches above the plant tops.
Easiest way of doing this, if you don't have a commercial light stand, is to hang shop lights on chains. Then, as necessary, you adjust the height of the lamps by moving them up the chain.
Alternatively, get a cheapie bookcase (the kind with the adjustible shelf brackets). Mount the light at the inside top, and then move the shelf up or down as necessary.
This past winter I grew these herbs under lights: Lavender, rosemary, oregano, parsley, chives and tarragon.
BTW, if you're in to micro-greens you can grow them the same way. What I do is set up a flat and start a row or two every couple of weeks, harvesting them in succession as they reach the size I want.  |