Blackcurrant pruning

Hello, I'm completely new to gardening, but i've happened to receive responsibility over a (pretty ancient and unkempt) garden and apparently more or less at this time of the year one is supposed to prune blackberry. Now, within a few days my area is going to see temperature radically hike up to 15°C, though the temperatures at night are going to remain just barely above 0°C.

The question is - should I prune it now, or wait still? How do you manage to do it right before the vegetation period anyway? Thanks.