I grow it but live in Houston and don’t know answer to your question. Very tough Plant and even when we’ve accidentally mowed down foliage, it comes back stronger than b4.

"How can the bulb and roots function in frozen ground? "

The same way the roots of any other spring flowering bulbs do. Soil temperatures never get as cold as air temps and in many cases, they seldom decline much below freezing. Prolonged or extended periods of subzero temps could alter that but that's more of an issue in the tundra or with permafrost than it is with the soil in a zone 6/7 garden!!

"Also how does it photosynthesize when there is snowcover?"

The same way any smaller evergreen shrub or groundcover does when buried in snow. Snow does not halt photosynthesis.

"The growing season is the total opposite for this lycoris compared to all other temperate climate plants."

I don't believe this is true :-) A great many plants feature winter flowers. And there are quite a few plants that are dormant in summer but grow, develop and flower in the "off season.

Leucojum aestivum?

Gardengal, but evergreen shrubs like lets say azaleas are dormant in winter(right?) so I thought they would not photosynthesize one bit of sunshine? People say protect conifers from winter sunburn which means they absorb no sunshine in the winter because they are fully dormant. Wouldn't that be the same for broadleaf evergreen shrubs as well?

Also if they are still undormant(not sure if its a word) as of now in february wouldn't the leaves have started growing back after being chopped to the ground? Just like how grass grows back after being mowed, and my sedums grew back after being eaten by deer. So I guess the MAIN thing I want to know.. what months are they typically in the active phase? I am guessing August(bloom time starts) to April/May(when leaves start fading)?

Oh I did not know that.. I always thought they go completely dormant even with some of its leaves on.

So I will watch my lycoris if they will start growing new leaves in spring. But then again it's close to their dormant period so it may not.. Some of the chopped leaves are already turning yellow and looks like it's rotting away.

I've only been able to take one horticulture class yet. My work schedule and the class times don't meet well which restricts me to take night classes only and they barely offer night classes. Also no weekend classes