It's hard giving advice to a hiker you don't know. In my experience (i like breaking tracks through nice fresh snow):
The JMT is often blocked at the switchbacks beyond where the trail splits off the Mist Trail. On some low snow years it may be passable. Crampons and a ice ax will help getting over the ice mound, but it's not worth it.
Getting up to Clark Point is fairly easy. Maybe a couple tricky short sections, no big deal. If you have a hard time getting to Clark Point, turn around, collect pizza and beer. Bivy and shoot up Snow Creek tomorrow, a better goal.
Beyond that, the cliff walls southwest of Nevada Fall are also filled with ice shields and inaccessible.
That section of the JMT is typically "closed." Often rightfully so.
Heading down from Clark Point to the foot of Nevada Fall is a good alternative.
That's the "open" trail, the mandated route of travel. No big deal. You lose some elevation and add some distance, factor that into your window. Light and shade.
Now may come the hairy. The switchbacks on the Mist as you gain Nevada Fall are steep; they can be icy. You are entering a known avalanche zone, which extends well past the bridge until you enter LYV. There are usually a couple big slides up there in a typical snow year. Just be mindful, nothing insane.
Chances are you will find tracks to follow. Of course, keep an eye on conditions & weather & have fun.
-Joe