Leave hydrangea flowers on all winter until you see the first signs of new growth in early spring - the old heads will protect the buds from some of the winter weather
Check which type of hydrangea you have before pruning in spring - the paniculatas [which is what that looks like from the pic] are different from mop heads or lace caps, and get pruned harder. They flower on new wood, as opposed to the previous year's wood. They produce heavier flowers, so they can become a bit top heavy if not pruned adequately
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Take a look at the RHS site for all the info
https://www.rhs.org.uk/advice/profile?pid=516
I live in west central Scotland - not where that photo is...