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It was trying to put out branches. Put the amputated limbs in dry soil for a while. Most euphorbias do fine Dec-Feb without any water.
Lots of Euphorbias are tough and tolerant except about water in the winter.
I don't think any special waiting period is necessary, as long as you don't water for a week or two. I'd just pot them up, put them in bright shade, and water sparingly over the winter. If the pot is small and the mix is light, it will dry pretty fast even if the plant isn't drinking. Wait until you see new growth on top before ramping up the water and light. Maybe in the spring. I water my Euphorbias over the winter, mostly with the goal of letting them dry in between each time, but of course your mileage may vary in a more severe climate.