Personally, I think Snape and Dumbledore had a big plan all worked out--remember their fight in the Forest that Hagrid mentions to the Trio? Maybe it was because Snape didn't want to kill DD, but Dumbledore was reminding him that he had to do it.
And remember how Dumbledore only took Harry along with him to find the Horcruxes when he promised to follow whatever DD said, even if he didn't want to? Methinks Dumbledore made Snape promise him the same thing...
PS: Some of the poll 'choices' reflect my poor version of humor. Ignore them if you get confused.😛