Post-boy:

"A boy or man who rides post; a letter-carrier." O.E.D.

Post:

"One who travels express with letters, messenges, etc., esp. on a fixed route; orig. a courier, a post-rider (now chiefly Hist.); a letter-carrier, a postman (now chiefly dial.). O.E.D.
It is possible that the post-boy regularly rides back and forth on the Cole Harbour Road, or on the Old Preston Road, and that on this occasion Louisa has flagged him down. But if so, one wonders why this is the only time she makes use of him. It seems more likely that he is an occasional visitor, riding from Halifax to Colin Grove to deliver the odd important letter. On this occasion, it seems that upon heading back he has agreed to take Louisa's notes for Harriet and Maria. Whether this part is done as a favour or for a fee, isn't disclosed.

In England, when the post-boy had a letter to deliver to a private residence, he blew his horn as he approached the house

"1672 R. Wild Declar. Lib. Consc. 4, I suddenly heard the Post-boy blow his Horn near my Window"--O.E.D. under "Post-boy").
If Louisa's post-boy rode up and blew his horn, it seems he delayed long enough to enable her to write her notes.