This question suggests an unusual amount of knowledge of royal messengering. Unless, somehow, it was common knowledge that a seal on an envelope sealed its authenticity. I mean, how many people actually received royal communiques? How many people had even seen a royal seal? But, Horatio is friends with a prince and even when Hamlet’s not there, he hangs around with royals so I guess he’s got a lot of insider knowledge of how this stuff works.
But also I wonder if he hasn’t secretly plotted such a thing and this question speaks to an obstacle he encountered, so he’s thought it through. Maybe.