Just because you feel strongly connected to a horse or a bird does not mean that either of them will be your spirit animal.Your spirit animal will only appear when you need them the most basically when the time is right.
They will also chose the form in which to appear to you as.This form will be a form you feel comfortable with and will acknowledge.It may not take a form in which you expect so be warned do not be disappointed if it happens.For myself I expected nothing and was content when my spirit animal revealed itself to me.
You should go read some more about spirit animals it will enlighten you and make you all the more eager to know.
As you are falling asleep, keep "meeting my guide" on your mind. I mean have it be the very last thing you are thinking about. Don't worry if it doesn't work the first night. Took me 3 times, and then I had a wonderful introduction in a dream. Good luck and blessed Be...
Best way to find your spirit animal would be to begin with simple meditation and visualization exercises, if you haven't already practiced them. Find a place in your mind, a place of nature where you feel like you belong. Don't try to will the spirit animal to come to you. Let the spirit animal comes to you, and it will come if you are intent. Don't be disappointed if you see it's small or not what you expected. It takes spirit animals a great deal of effort to get out of their comfort zone and reveal themselves to you,