Rips, inbreeding is referred to as the breeding/pairing of direct relations- brother to sister, mother to son, father to daughter. People don't do that currently, but if you look in the exceedingly common Tb or QH lines (allbreedpedigree.com), you will see that not long ago, not many people really cared to much to check just HOW related they were.
The bad effects are less so with half siblings/half relatives, but I would not do it.
As someone who wants to breed horses eventually, I wouldn't be put off of searhcing high and low for desireable traits outside of the line. I'm in NorAm, so that may every well mean searching in the smaller european countries for farm studs, but so be it. I would flat out refuse a breeding to any relations within 4 generations.
Welsh are not that bad. Technically, niether are QH or Tb horses.
You know it's bad when there is an inbreeding PERCENTAGE on a horse, specifically the friesian breed.
And yes, you need to inbreed to re-populate. We all came from maybe a handful of 'sires' ourselves, as did the thoroughbred. Just look at the cheetah as well.