You are still on track to get blooms with ES. Some deadlooking stems will probably be dead but some may delay leafing out so wait until mid-May to make sure. This often happens on year one of newly planted hydrangeas as a result of the way the wholesalers prep their plants for sale the year before. It makes them start blooming at un-natural times on their first Spring.
But new shrubs are not the only ones affected. I am currently monitoring the effects of my last winter as I noticed many of the Macs (like your ES) and arborescens having quite a few dead looking stems this year while the oakleaf hydrangeas look as if there were no wild temperature swings and are fully leafed out showing no damage.
Arborecens tend to be the most winter hardy of the three types of hydrangeas that you mentioned (up to Zone 4); oakleafs are next (up to Zone 5) and macrophyllas like ES are last (up to zone 6 but some are more tender, hardy to Zone 7).
If you see no change by early to mid May then feel free to prune the dead sticks from the ground. In case you are curious and want to know if they will bloom, you can prune from the top downwards in 1/2" to 1" increments; stop when you get to the bottom or when you see green. However, if there is green, this type of pruning could end up cutting any flower buds left on the stems. Flower buds are usually invisible so you cannot tell ahead of time if there are any flower buds at the end of the stem so, consider "the chance of pruning off the flower bud" as the price one pays for finding out if the stem will leaf out or not.
Since ES is a rebloomer, I would expect the new growth to develop flower buds and flowers later in the season. If the ES stems were to leaf out from the dead looking stems, you may get bloomage -example- by the end of May but, if those stems are dead, you need to wait for the new growth to develop, grow and... your first set of blooms will be in late June or thereabouts.
To prevent the plant from being affected as bad in the future and to allow the old wood to survive and bloom, you can: winter protect the hydrangea, water its soil the night before a freeze warning is issued (but do not water once once the soil has frozen), maintain 3-4" of mulch at all time up to the drip line and stop all fertilizers by the end of June or so.