Keep them in until the walk is done
The morning after a storm is when patience pays. Horses turned out hungry and fresh into a damaged field will find the damage for you — through it, over it or impaled on it. Hold turnout until each field has been properly walked, even if that means hay in the stable and a later, shorter day out. The check has to happen in daylight, on foot, at walking pace; a glance from the yard gate or a slow drive past in the truck will miss exactly the failures that matter, because storm damage is usually a single post, a single strand, a single corner.
Walk the line itself, not the view of it
Start at the gate and walk the boundary with your hands, not just your eyes. Push every post: a post can look perfectly upright and be snapped at ground level, rocking loose in a saturated hole. Check rails for splits and for fixings pulled out of posts, and check wire for tension — strained wire gives its damage away at corners and strainers, where posts lean inward and insulators crack. On electric fencing, follow the tape or rope looking for fallen branches resting on it, broken insulators, and places where the line has been pressed into wet ground and is earthing out, then confirm the fence is actually live before you trust it to hold anything.
Trees, water and the damage storms leave behind
Fallen trees are the obvious hazard, but look up as well as down: hung-up branches and cracked limbs widow-makers waiting for the next gust can come down days later into a field full of horses. Walk the gateways and low corners for washouts, where running water has scoured the ground from under a fence or turned a gateway into a bog deep enough to trap a leg. Clear debris that has blown in — sheet material, plastic, broken branches — and check water troughs for contamination and for automatic fillers still working after power cuts and pressure surges.
Repair it properly or fence it off honestly
Divide what you find into "fixed now" and "fenced off." A broken rail can be replaced on the spot; a long run of damaged wire cannot, so put a temporary line of electric tape inside it, far enough in that horses grazing up to the tape stay well clear of the wreckage. Prioritise any boundary that fronts a road, because a loose horse on tarmac is the worst outcome of a storm by a long way. Do not convince yourself that one strand of tape at knee height will hold fresh horses who can see the gap in the real fence behind it — it will not, and they know it.
Check the animals and the buildings too
Before turnout, look the horses themselves over for the storm's other souvenirs: cuts from stable doors banging, swellings from a frightened scramble, a horse who has gone off his hay after a night of thunder. Run a hand along field shelters and stable roofs for lifted sheets and torn edges — a loose roof sheet develops sharp metal edges and a habit of travelling in the next gust. KinsLe Family Sharing gives relatives you pick access to a horse's profile, for a relative helping with evening feeding after the storm checks.