How to install invisible pet fence in frozen ground?
First thing first, do NOT use a reciprocating saw for this as this is dangerous and you could end up seriously injured.  

If looking for something to make this easy, what you need is a trencher - you can probably rent one from your local home improvement store.  It will look something like this (there are smaller models but I couldn't find a good picture).  If you can't rent one, maybe try contacting a sprinkler installer to see if they could come do it for you.



EDIT: Found a smaller one, looks like this:


(source: terrasaw.co.nz)  

Alternatively, as others have mentioned, you could just lay it on top of the ground for the short-term.  And of course, some back-breaking labor would also accomplish the job.