Hi, Sharon. I think most of the cooks on 52 are down on infused oils due to one problem, possible death from bacteria (not the good ones) growth. If you search back in the Q&A section, there is quite a bit of wisdom on this. I'm not an expert, so I'm guessing.
Olive oil should never be frozen nor refrigerated. If you are going to use infused oils use them as fast as possible. Of course you could also die from eating hummus from Trader Joe's.
For years I have been filling ice cube trays with fresh herbs from my garden in the summer and fall and then topping with olive oil. I freeze them and use them for everything all year long. This isn't exactly what you are asking about. But with clean herbs and equipment, I think you will be fine.