Cp69 - Yay for you! And what a great opportunity to be able to pursue your education with the financing provided.
I don't think 38 is a big deal. (I know all the 20-somethings around here think we're ancient but they'll learn!

)
I'm 46 and started back just this fall to complete an education I abandoned 24 years ago. And yes, it includes science.
I'm finding that I'm a much more focused and disciplined student than I was a couple of decades ago. (Then I was definitely more focused on boys and parties!) I am much more familiar with my unique learning style and can tailor my studies to optimally benefit. I am very clear about my goals, I know what I have at stake, and I'm passionate about what I'm doing.
As for Doku's point of your chosen program taking 7-10 years - you do need to look at the big picture, but determine how important is this goal to you? How committed are you to seeing it through to completion? And finally - if you're thinking about the age thing - How old will you be in 7-10 years if you DON'T go to vet school?
Lots of luck!