Now, I'm no freestyle expert. Frankly, I've never done one. BUT I am saying these things based on all the ones I've spent watching on YouTube (heehee).
My biggest qualm poorly blended or chosen music. I know we can't all hire a professional to mix things up for us, but make you get several opinions from both horsey and non-horsey people to A) see if the music flows well, B) goes well with the horse's movement (a note on that below), C) has a nice beat that you and your horse can keep up with.
On B, I have seen some people do "inside joke" music: the music fits the horse's personality, BUT in no way does it fit their gaits.
I won't go on that much further, because I'm not an expert haha!
For the big, bold, dramatic mover: pick something that is just that, big, bold, and dramatic! And please, no 'Pirates of the Caribbean' music. Overdone. Same goes for 'Dancing Queen' lol. There is a lovely track from the 'King Arthur' soundtrack called "Another Brick in Hadrian's Wall". Move a little bit farther into the music and you get some wonderful bass and percussion and dramatic orchestral pieces, starting at about 0:45. It even starts to get a nice beat for a big canter.
The 'Avatar' soundtrack also has some really cool music, and if you want to add an exotic touch without going too tribal, this is also a good place to start. This is one of my favorites, and an iconic piece from the movie, called "Climbing up Ikinmaya - The Pathway to Heaven". There's a subtle beat of the maraccas in the beginning that could do well with a working trot or canter, and some of the percussion beats later on would work well with collected trots or passage, and the choral climax towards the end would do well with a burst of an extended canter.
These types of music seem to do well with a horse that has big gaits, but not very defined or snappy or electric ones. Think a big draft or heavy warmblood, yah?
For the more electric horse: there's all kinds of fun things you can do! I had a friend who said she had trouble with her horse's electric gaits for a freestyle (Oh, whatever shall we do?!) She had some songs she liked, but she couldn't find songs with a consistent, snappy beat that would highlight her horse's gaits. I said, "Have you looked into remixes?"
NEVER forget to look into the remixes of songs. Let's take a lovely song called "Cosmic Love" by Florence and the Machine. A great song, but not very many parts of a consistent beat that a horse could work with. PEST has an awesome remix. The very beginning, if mixed up and repeated, would do very well for a canter, as well as most of the song. Maybe not for all the gaits, but it's a place to start. The good thing about remixes is that you can take a song you like that may not have a steady beat, and find one that does have a steady beat.
And for the Gaga lovers, there is a great remix of "Bad Romance" by Starsmith. There is plenty of play with the beat in the song, so if mixed right, could serve all the gaits and be very electric at the same time.
AND there is a wonderful style of music from the other side of the world called Bhangra and Bollywood. Don't believe me? Check out this song called "Discowale Khisko (Move Over Disco)". Need a remix? There's one on the soundtrack lol! Although I think the beat is a bit quick for a freestyle, but who knows?
Another bhangra beat that sounds both Western and exotic is "Majajne" by Suskshinder Shinda. Look at music from around the world! You can find some cool stuff.
For the cute mover: this is a bit easier! Rock n' Roll songs and most pop songs sound really cute. Try some Brit rock like The Ting Tings or Two Door Cinema club to spice things up a bit. "Shiver" by Coldplay would sound good, or perhaps "Wake Up" by Arcade Fire. Really, now is the time you can mix and match some of your favorite pop songs. You want to have some fun, make sure not to play down your horse's strong points, and keep it appropriate. Here is some lovely inspiration from Catherine Haddad. Granted, Winyamaro is not exactly a cute mover, BUT the song usage is fun and a great idea!
That last example is also a great reminder to look for instrumental versions of songs (like those P!nk songs) on YouTube. If you like a certain song but the lyrics take away from the performance, guarantee that some techie out there has taken that song pulled the lyrics. They are EVERYWHERE! Like the instrumental version of Coldplay's Strawberry Swing. Cute, cool, classy, and calm. Of course, the lyrical version sounds great as well!
P.S. that last song is what I would love to do a freestyle to. I have yet to look and see if it would fit Greta, though. It might not!
Those are the ideas I can think up of. Let's get some freestyle input brain juices flowing!