This is some really nice land. And since it's turn 11 and you still haven't even met an AI, you probably don't have any
really close neighbors.
Your warrior has a lot to do where he is now. Something like S (check coast tiles in case of seafood), NW, NW (big vision radius from hilltop, some defense bonus, scout a lot of important land). Then if you don't see any barb animals around you could try going something like N, NE. By the time it's done all that
and move back to your capital, it wouldn't be getting out to scout the horses much faster than simply waiting for your second warrior to be built and sending that one out to do it. Once it's poked around the west a bit it can either feel adventurous and keep exploring, or it can find a nice safe spot to settle down where it will not die and will prevent barbs from spawning in a 5x5 box centered on it - hopefully pushing more spawns away from you and towards other AIs instead.
I'm liking the worker - warrior - worker - settler suggestion here; there's a
lot of forest to clear, and this is not a situation where you're worried about being choked out of any good cities. Your capital is great, you've got a nice pocket site to the south, you've got two spots to the west and probably somewhere to the east, and you're Egypt with fairly accessible horses and tons of forests which means if there
is a nearby AI who starts taking your preferred city sites you just chop out some war chariots and conquer them. You want to get that second city out fast because you want it contributing fast, not because you're worried the land will all be gone; the second worker will also be contributing fast so you can delay the city.
But if you're thinking second worker before settler, I don't think you want to skip the cows entirely. That's putting a significant production burden on you for getting out your settler, and delaying the cow pasture until after that's all done is going to slow you down more than it helps.
I'm not sure about cows - pigs - gold or pigs - cows - gold; the former saves 2 worker-turns, which is very nice, but at the cost of delaying your city hitting size-3 by a few turns and thus delaying your
second worker a little (net-neutral on worker turns at best). It lets you get out some more early warriors as "freebies," but as
@Fippy noted you don't really need more than 2 warriors early on Monarch so they'll basically just be sitting around doing nothing for the next 15-20 turns. My inclination is to avoid trying to be too elegant and just do what's natural: improve pigs, then cows, then gold.