I'm sure the plants are quite old but they can be removed. If you can pull it them out with a truck or tractor - that is your best bet. The roots will break off at some point, you can't get them all without major digging, but its okay as juniper doesn't readily grow back. A better question is do you have a plan for what you want to replant ? The soil will need to be amended and enough of the junipers roots removed to allow any new plants to be successful. Perhaps you could just prune the junipers back to an acceptable shape.... ?

We've been removing our juniper a bit at a time. First we trim back those leggy branches and get as close to the trunk as possible. I wait for the trunk to die and then work my way into snipping the roots. I agree that the soil needs to be amended afterwards. Also, you should have a plan on what you are going to plant in its place. Tons of weeds just took over the area afterwards.

I put on protective clothing and go after those bad boys with a reciprocating saw. They're history in no time.

We just removed a lot of 40 year old creeping juniper. We pulled a lot out with the truck We had to cut huge roots. It is a lot of work. We hauled off 4 dodge trucks full today and still have more to go.