Translation:The woman gets a horse from her husband.
I'd say (as a Yorkshire woman) that the main issue here would be the dissonance between the fairly formal "receives" (as opposed to "got") and the dialectal "off", which I might well use in another context. The meaning is also slightly different: to get something off someone implies a certain degree of (maybe friendly) coercion or even amicable trickery!
It doesn't mean exactly the same. Kvinnen får en bok i posten FRA mannen sin. In this sentence you would use FRA because it comes from somewhere. AV is more like he is giving her something. Kvinnen får en bok av mannen sin til jul. Here it is like a gift is given to her, then you use AV.
av means both 'of' and 'off' e.g. å bite av - to bite off
In fact, 'of' and 'off' came from the same OE preposition 'æf' and were later reanalysed as two separate words. This change didn't occur in the North Germanic languages.
Therfore, 'kvinnen får en hest av mannen sin' is word of word 'the woman gets a horse OFF her man'.