Well, here is what I remember from genetics class - forgive me if I'm rusty:
The mare and stallion each provide 50% of the genes to the foal, with the exception of mitochondrial DNA which is always transferred from mare to foal in the egg. Mitochondrial DNA has to do with cell metabolism and things like that rather than the typical physiological traits. So technically a foal does get more genes from the mare, but not generally affecting visible traits we are talking about.
As in any other cross of two parents, the visible traits have to do with dominant and recessive genes,the consistency of his/her own genetic makeup (heterozygous vs. homozygous for each pair of alleles), and the incredible number of combinations that can occur in the sex cells of the parents. This is where in/line breeding can create prepotency for traits, whether good or bad. The more homozygous or dominant the parents's genes are- the more likelyhood that the foal will get the trait. Some horses have many dominant genes for certain traits and their foals most often will express those traits when bred to another horse with less dominant genes. For example, a mare that always has produced straight legs when bred to various stallions is likely carrying fairly dominant genes for the numerous physical traits that produce straight legs. She may, however, always produce the head of the stallion or one that is better or worse than hers.
In my opinion it is not as simple as 50/50 and is not always 80/20 or any other percentage. It boils down to the consistency of genes that each of the parents got from their parents and the relative dominance of the genes over those of the other parent.
Now to muddy the water even more...Visible traits of a horse can be genetic or environmental. For example, straight legs are more common in horses that are properly trimmed and in horses whos parents have strait legs. Some horses that would have normally have straight legs can go crooked becasue of poor trimming and horses with poor leg conformation can often be improved with good trimming. The behavioral traits such as personality and herd status are likely hugely affected by learned behavior and therefore these traits may follow the mare (with whom the foal spends more time)more often than the stallion.
Ok,so even if I got all of this information fairly correct it doesn't answer your question because it always depends on some factors that you cannot see. It is dependant on each horse. The only way to know how consistent foals are out of a mare or stallion are is to have lots of foals with many different pairings and look at the results.
Or maybe the mare does give 80% to the foal.
That would be way less confusing and complicated