Little Lord Umber was sent to Last Hearth (home of the Umbers) to collect more fighting men (and, I assume women and children) and bring them back to Winterfell for their safety and to shore up Winterfell's defenses.
He was found nailed to the wall at Last Hearth.
Unless I am mistaken, the Night King broke through the wall at, or near, Eastwatch by the Sea, so it makes sense that Last Hearth is between there and Winterfell, which would explain why Tormund/Dondarion, who would clearly be behind the dead army, would get there after the Night King. A lot of defenders died when the Wall was breached, but part of the wall still stands on either side of the breach, so (clearly) some defenders made it to safety before the collapse.
In theory, Umber went to Last Hearth on horseback. The dead army is mostly on foot, so would take significantly longer to get from there to Winterfell. Tormund, and his buddies, are going to be on horseback and try to go around the army and beat them to Winterfell to warn them of the army approaching.
Here is what doesn't make sense to me. Why would Edd, and other members of TNW, go from Castle Black to Last Hearth? Wouldn't they take the straight shot down the King's Road and go to Winterfell? Their presence there was not explained and seems illogical.
With all of that said, transit time made sense in the first few seasons, but doesn't come close to making sense in the recent 2-3 seasons.