IF THE TREE IS ALREADY DORMANT--and it's small enough, you might actually get away with putting it in the refrigerator until March or so--HOWEVER, the temp inside must remain below 40 F--ideally below 35 F (which is probably one of the colder settings) additionally, the tree must be kept humid. Refrigerator air is bone dry and could dessicate or dry out the tree's tissues over time. You could place the tree in a big gallon sized Ziploc bag, but you'd have to air it out occasionally to prevent mold and mildew.
If the tree is not dormant, putting it in the refrigerator will not make it go dormant and it could also be significantly weakened or killed. I'd also be very careful about where it is placed inside, since having a 5 lb gallon of milk smashed on top of it, or having it greased by a nearby stick of butter won't do it very much good.
Wait to store it until after all the leaves have changed and have fallen off.