Cut out dead or damaged or weak shoots and reshape in Spring, as growth begins. That looks like a mature olive, obviously planted in the ground - there's little you can do to provide protection during severe winters other than attempting to erect a shelter of some kind over it. If we return, this year, to the sort of winters we've had for the last 15 years or so, the tree will be fine - just depends whether we keep on having severe winter weather.

We lived for a few years on an Olive farm in North Eastern Spain and experienced one or two snowy winters there. We had to prune severely, but the trees were fine. In our area the trees were pruned into a weeping shape...making the collection of fruit easier.....this involved cutting out weak and upright growing shoots.....they were beautiful, looking like large Bonsais....:o)