Put on a pair of gardening gloves to protect your hands from scratches.
Trim any branches that have broken away from the main shape of the arborvitae with a pair of pruning shears. Make the cut where the broken branch meets the rest of the non-damaged branches instead of where the branch meets the trunk to avoid giving the arborvitae a thinned out look.
Make your way around the entire arborvitae until all snow damaged branches have been trimmed to match the rest of the plant's shape. Only cut away branches that have been broken by the snow damage.
Tie a length or two of heavy string around the entire arborvitae to hold up branches that have been simply bent by the snow damage. Sometimes, these branches will begin holding up again on their own, and others will bounce back once spring arrives.
Remove string when the shrub has stabilized.