So draw up to 6 then trash one is basically Masquerade, which is a very powerful $3. So this has that plus a Militia attack; sounds too strong for $5 maybe.
The reaction is a neat concept; but it has a problem.... "when you have fewer than 4 cards in hand" is not an event; it's a situation. When exactly do you use the reaction? At any moment? There needs to be a specific event that it's responding to. It could be "when you discard or trash a card from hand, if you have fewer than 4 cards in hand..."
Personally I think there's a lot more going on with Masq than just "draw up to 6, trash a card from hand". I guess drawing up to 5, then discarding/trashing would bring it more in line with Militia, but still a little stronger since it can sift and trash.
What if the event was "When a card leaves your hand, if you have fewer than 4 cards in hand..."?
Edit: Oh hmm, that's interesting... if Horse Archer only draws up to 5, then trashes/discards 1, then it's worse to have it trigger at the start of your turn, as that just takes 1 card from your hand. Maybe it'll be better to just increase the cost to $6...
Edit2: Actually yeah, I got a little overexcited on the idea and I admit to not thinking it through much. The trigger is interesting and I'd like to explore it for another card, but it's too powerful for this one. I'll pare Horse Archer down a bit but I'll leave the old version there for context.