How long after Botox will I be able to wear a horse riding hat?

Botox takes about 4 hours for the botox to be fully in the muscle. If your riding is tight i would recommend waiting 3-4 hours, if it fits loose then you will be fine to wear it immediatly

I see no contraindications to wearing a horse riding helmet after receiving your Botox injections. It should not affect your treatment.

Different physicians will most likely have different opinions of when you could wear a horse riding hat after a Botox treatment.  Personally, I would say you could wear the hat later the same day, as I do not believe it would affect your result.  If you wanted to be extra cautious, you could wait a day.  

For most patients, there are no restrictions following a Botox treatment. Sometimes patients will use cold compresses immediately after injection to prevent or lessen swelling and bruising but wearing a hat typically does not present any issues.

I am an equestrian and a dermatologist, have Botox treatments now and then, and I ride 4-5 days a week, so I am quite familiar with your dilemma.  I see no reason for concern or delay.  Wearing a helmut that fits properly and not excessively tight should not affect your treatment significantly even the same day.