Leather was widely used in the Viking Age. Shoes were worn partly as a status symbol as much as for comfort. The illuminations from the period show people working in the fields barefoot. This is a purely practical consideration, since all the careful work the shoemaker or your father had put in to cutting and sewing the shoe would be rapidly undone digging the fields over. In addition the workers are also shown to be trouserless for the same reasons. As a young child you may not have worn shoes and gone barefoot, mainly because you would have grown out of them fairly quickly creating far too much work. The only exception to this rule of thumb as usual would be the wealthy.
There is some suggestion that people may have removed their shoes when entering higher status buildings much in the same way that the Japanese do today as a mark of respect. The evidence for this comes from ivory carvings depicting various scenes from the Holy Roman empire. Caution ought to be taken in assuming that this was widespread, because these carvings could once again be a hangover from older or more stylised carvings that were subsequently copied.
It's uses didn't stop at shoes. Bags, belts, scabbards, pouches, harness and when oiled even some garments would have been made from leather. It is where we get the name for oil-skins from. They are perfectly waterproof, but heavy and lack any form of insulation, necessitating warm woollens beneath.