3 years is a reasonable contract out of the gate for most coach who still has to establish himself. That in itself is considered a "multi-year" contract. The things Horton has going for him are basically 2 big wins at the end of the season and stabilizing and renewing confidence in the team. His previous record as a HC is not good at all.
Though he did very well at the end of the season, I am not certain that is deserving of a 4 or 5 year deal. Given another year or two, we can see how the team fares under him over a period of time, the recruiting he does and the overall direction of the program. The contract can always be renegotiated.
Like I said, he has basically 2 wins going for him...I think my suggestion is reasonable if they are going to hire him.