Its a pachypodium, probably succulents would be your forum, but, they are deciduous if they get too cold, so yours might have just dropped its leaves temporarily, if it got any frost damage it will show up later as rot.

They should be fine, I would not water again until you see new growth starting, which may not be until the weather warms up and light intensity increases, sometime in the spring.

Pachypodiums normally go through a dormant period where they lose most if not all their leaves during what should be a dry, cool winter rest. They will rot if kept cool and moist.

I agree 100% w/ xerophyte. Leave it alone and treat it as a cactus in the winter. Don't water it and when Spring gets here, set it in the sun and when you see new tiny leaves starting at the top, then water.
I have four of these and they are beautiful, but in the Winter, it's best not to "Mother Hen" them.

Thanks. I haven't watered it figuring that would probably cause more harm than good. I have it in a cool downstairs room with some dormant plumerias and brugs and have been treating it the same as them, pretty much ignoring it. It was such a beautiful, albeit dangerous plant last summer. I'm pretty sure the trunk didn't suffer any frost damage, just the foliage.
Karyn
This is what it looked like in Sept, now it's just a trunk : (
{{gwi:345421}}

Karyn,
I had one that was almost exactly like yours! Same height, same double trunk. I bought it as a 4-5 inch plant from Home Depot many years ago. I had it in the house for a long time, then out on the porch, then by the pool, then, in a moment of absolute stupidity, I planted it in the greenhouse. From that day forward it was a battle. Everytime I turned around in that area, literally, I backed into it! And got thorned in the butt! I have a few small scars from it. I put up with it for a season, then decided to dig it back up and use it as a houseplant again. But alas it was not to be, it resented the move and ended up expiring. Seeing your photo reminds me of how much I really loved mine. I am going out today and get another from Home Depot, thanks for the inspiraion!

Reminds me , that someone asked me, though I've never grown one, why hers , which she's had for quite a few years, never flowers? I could only guess they need a cool and dry, though still sunny rest in the winter months to flower well?

The one that is pictured to my knowledge has never flowered. It had been in a corner of the greenhouse for a number of years, completely ignored (don't ask how I could have overlooked it for such a long time!)I rediscovered it a couple years ago and brought it to the house and have kept it on the deck during the summer and back to the GH for the winter. I'm just hoping that it puts out new growth when it warms up. I've really developed a liking for this plant even though I've been speared more than once. It almost caused a car wreck the day I took it home from the GH. My toddler and dog were in the back seats of my van so I put it on the passenger seat for the trip home. Big mistake! I rounded a turn and the trunk went into my right arm and leg (I was wearing shorts!) I should have turned around right then and put it back in the GH. Who knows, if it's not irreversibly damaged maybe the cool winter temps will make it bloom this year?
Karyn

Thats the tree, then I am about 99.9% sure it will be fine. One that mature, it would take a real good freeze to kill it.

Pachypodiums are in the same family as Plumerias, a certain age is needed before flowering will occur, as well as a long growing season with warmth and regular moisture, and a short, cool, dry rest to initiate bud formation followed by leaf growth- it is tricky to get the plant enough light during those critical short days, I have a Pachypodium brevicaule that has finished flowering a few weeks back, the buds did not form until after it was kept dry and cool for several months; flower buds will abort if moisture is not light and regular.

x

Xerophyte I just googled images of the Pachypodium brevicaule. What a cool looking plant and the flower is quite similar to a plumeria. I've never seen one before. Are they easy to find at a nursery? I couldn't find a good image of a Madagascar palm bloom. The cool room that it's in now is lit with a couple 1000 watt HID lights so maybe it will have had the proper conditions to force a bloom this season. I got as close as I dared to the trunk and can see green tips so I'm pretty confident that it's alive though I don't see any new leaves yet. Will it come out of dormancy the same way my plumies do and should I treat it the same as I do them?
Thanks,
Karyn

Hopefully this works. Just took a pic of mine by the pool..
http://i209.photobucket.com/albums/bb212/TopekaPalms/Picture-6.jpg