Can I hook up a subpanel to an existing 220 line that isn't in use?
Yes you could go with your plan but most of us will strongly suggest a larger panel. As it is for outside circuits everything will require GFCI protection. If the box or panel location is outside the panel will need to be rated 3R (for outdoor use). 
But yes you can do as you have planned. 
If the panel is not located on the house an additional grounding electrode will be needed.