I understand your reluctance about horseriding, but for my DD it was the best thing we ever did.
She was also 'clumsy', took ages to learn to ride a bike and was 'unco-ordinated' so couldn't catch/throw/kick balls etc
Over the years, we had her at classes for (at her request) swimming, badminton, ballet, tap, trampolining, ice skating, roller blading, rainbows, brownies, guides and judo. Some she did for a few months, some until she completed the full course (which took years i.e swimming and guides etc), some she did only a few times, or until she had advances a few 'levels', and grew bored so stopped.
She wanted a 'horseriding' birthday party at 6yrs old, which was VERY expensive (so was very small too !) but she LOVED it. We spent the next 12yrs attending lessons once a week (which other family members very kindly contributed to).
She still kept up with some of the other 'hobbies' like Rainbows, swimming and others (cheap ones or 'important' ones like swimming)
She also put birthday/Christmas money towards doing all the different Summer Camps they do, where they work their way up the levels etc (as well as progressing through the riding levels with her weekly lessons etc)
Over time (once she was 7 yrs old and knew enough about how to care for a pony etc )she began to participate in being a 'helper' at the stables, so she could 'earn' riding time (most stables have a helper scheme where they help skip out/feed/groom etc to earn riding time), which meant that as she grew, she earned her own lesson time, so we didn't need to pay much at all.
Fast forward to today, she's 20 yrs old, just finished her 2nd year at Uni doing Equine Business Management degree and works as a Junior Coach at the same stables, which gives her a couple of hundred pounds a week and fits beautifully with her degree.
You never know how your DD will 'take to' any sport/activity etc, but if you can expose her to as many as you can afford, then she'll find her 'niche'.
I would never have thought my very 'unco-ordinated' DD would've chosen the sport she did, and that it would've ended up being the career she wanted to pursue, but that's what has happened.
Give your DD all the experiences you can, and let her choose what she is drawn to.