At the risk of sounding rude (which I hope I don't in questioning this), I'd just ask, are you sure it was cold enough inside your school for parts of the plant to freeze? If so, brrrrrrrr. If temperatures drop under 40 degrees, I don't keep my jades outside at that point, and jades certainly are not frost tolerant, but I would be surprised if your inside temperatures have dropped below 40? But maybe they have right next to a very old window during the winter. I only question it because other factors could cause parts of the plant to die off, and the plant may not have been at optimum health to begin with, based on it being indoors and not having big, healthy roots.

It sounds to me, based on details such as your saying the root system is small, that the plant is probably not in well-draining soil and that it's possibly not receiving enough light (they don't thrive as indoor plants). Parts of the plant dying back and leaf loss are indicative of a situation where the roots are unhealthy (confirmed by a small root system), and rot could happen as the roots continue to die off. And no, there won't be a stench with the rot. If the root system is small, that's perhaps the biggest indicator that the soil is too heavy. If it's in bagged soil, even so-called "cactus soil" from a store or nursery, that won't be well-draining enough. You'd want to mix well-draining ingredients like pumice or perlite into that soil to lighten it.

Also, it's important not to overwater. I wait until the leaves have a very slight give to them--the plant will actually tell you when it wants water. You don't want to wait until the leaves are wrinkled or anything close to, but you can learn to feel the leaves and discern if they are barely less plump than they are normally, and at that point I water and the leaves plump up again. And again, in the wrong soil the plant will retain way too much moisture for too long, so that'd be the first issue to look into.

This post was edited by teatree on Fri, Jun 28, 13 at 20:27

Don't worry it wasn't rude :) Actually our res was too hot so I cracked a window so I didn't boil not expecting it to get that cold it would kill parts of my jade (I had no problems doing it the year before) Woops!

Anyways I took your advice and I transferred it over into new better draining soil. I also added some small rocks to the bottom of the pot to hopefully help some more with drainage.

I also discovered that the root system is actually smaller but was wrapped up in the dead roots of the two stocks I lost earlier. So hopefully with those gone these roots can finally grow out easier.

So far it seems to be doing a lot better, no more leaves are falling and I have a couple that fell off (and didn't end up rotting before the repotting) sitting in the soil and with any luck I can get a few Jade babies :)

Rocks at the bottom of the pot reduces drainage, so I'd remove those immediately, and pot the plant again.

Josh