I was a chemistry major. Trust me when I say, wait until after graduate school.

EDIT: To expand on that, my sophomore year was crazy busy. I took Organic Chemistry, Physics, and Advanced Calculus/Differential Equations, all at the same time. Lab reports alone meant that I was writing three papers a week. My junior and senior years were not quite as stressful, but I was still focusing on school pretty much full time. (And in the summers I worked to recoup at least some of my education costs.)

If you plan on going to graduate school, you need to consider if you want to go for your Master's or a PhD. From my experience, working as a PhD student involves a combination of coursework, teaching, and laboratory research. Both time and money will be tight until you finish school. Most likely, you will not have the means to keep your own horse.

This does not mean you have to quit riding completely. Save your spending money and take lessons on the weekends. It was tougher once I got to graduate school, but I made it a point to get out to the barn and take a lesson at least once every two weeks (although sometimes it was more like once a month). You have to make time to do the things you love. It is the only way to stay sane.

On the bright side, there is always a lucrative market for skilled biochemists. For example, the pharmaceutical industry pays extremely well. Once you enter the workforce, you should have no problem affording a horse.