Sandra,
Yes, military records for Austro-Hungarian soldiers before 1867 are available and fairly easy to research. Austria was involved in numerous wars prior to 1867 and so it very likely that you could find some of your ancestors. Once you find the personnel records for one, you can then research what his unit did while he served by locating the regimental history for it. These histories are very detailed and provide a wealth of information.
Here is a link to a website that will explain how you can go about it.
http://ahmilitary.blogspot.com/2011/03/guide-for-locating-au...
If you have any questions, feel free to contact me directly.
Carl