I would say to prune it while it is dormant. Sand won't help your St Augustine. They recommend a 3-1-2 ratio fertilizer for it such as 15-5-10. You could also spread some compost on it such as Cotton Burr or some bagged cow manure. Good luck on getting some rain.

Thank You wisner.

i would not prune while dormant. becasue it while then have tender tips that can freeze easily and kill the olive tree.

If u are pruning back to a branch or trunk u can do that any time and that is called thinning I think. If you are tip pruning or "heading back" I think it is called, that is what stimulates new growth that would be tender when it comes out and would freeze when the frost/freezes come. However, I never really understood why that was such a big problem, it can just be pruned off in the spring. Except it would look bad and maybe get a fungal infection or something being damaged. Really if it's an established healthy shrub/tree, I think it would take the pruning anytime. If you decide to wait until spring, then make any heading back cuts lower than you want the final height becoz u will stimulate new growth.