To answer your questions:

1. Yes, you always shuffle the deck after searching it.
2. If you get a gadget horse, you will have to invent it as normal with a mad scientist, but do so immediately.
3. As to whether or not the card is worth it, it's not bad on it's own, but the existence of Maggie Harris makes it a bit obsolete.

Also, if you're running a lot of horses you probably want your 6 of clubs spot free for Calling the Cavalry.

If you don't have those available, however, this is a fine way to get horses out on the board if your deck depends on them, and it fits into your shooting structure. Make sure there's a good reason to include it rather than just including more horses though.

I want to like this card but I have a few questions.
The first question is does the player shuffle the deck after searching? If the horse is a gadget, like Mechanical Horse, can it be played right away or should the player wait for the next time to act? My final question is would one ghost rock be worth pulling a card from your deck or discard pile?