Excluding Severus Snape, are there any Slytherin House members of Order of the Phoenix?
If not, why not?
Obviously, Snape was a Order member and a Slytherin. Even if we discount the most prominent example of a Slytherin Order member, there may well have been others. Many, indeed most, of the Order members (particularly the ones which are mentioned in passing from the First Wizarding War) don't have their Hogwarts house specified in the books. These people include:
This probably isn't an exhaustive list. Any one of these people could have been a Slytherin. We just don't have a specific example of another Slytherin Order member from the books, other than Snape. That doesn't mean that there weren't a couple of Slytherins within their ranks.
(Of course, remember that alongside actual Slytherins like Snape were people like Sirius Black, who wasn't a Slytherin himself but came from long line of Slytherin-only wizards.)
Assuming there were no other Slytherins in the Order, why might this be?
The out-of-universe answer is, as ever, that Slytherins are the bad guys and Gryffindors are the good guys. This may be stereotypical and one-dimensional but that's how Hogwarts houses seem to work. Wizards like Pettigrew and Snape who bucked the trend were the exceptions, not the rules. Although perhaps it's not altogether surprising that an organisation which was characterised by gallantry and daring in standing up to Voldemort was largely populated by Gryffindors.
In-universe, it seems that Slytherins are none too keen on fighting Voldemort. Judging by the Battle of Hogwarts, at any rate.
Slowly, the four tables emptied. The Slytherin table was completely deserted, but a number of older Ravenclaws remained seated while their fellows filed out; even more Hufflepuffs stayed behind, and half of Gryffindor remained in their seats, necessitating Professor McGonagall's descent from the teachers' platform to chivvy the under-age on their way.
(Deathly Hallows, Chapter 31, The Battle of Hogwarts).
The vast majority of Slytherins didn't believe in fighting Voldemort and so obviously wouldn't have been interested in the Order.