Ttyjukl

In Deathly Hallows Snape and Ron both independently find Harry and Hermione in the Forest of Dean.

Ron found them by using the Deluminator to approximately guess their location.

Snape found them after getting a tip-off from Phineas Nigellus.

Both of them were operating on Dumbledore's orders and using the means of finding Harry that Dumbledore had given them. Both of them were trying to find Harry in the forest, without being sure where exactly he was. Both of them were wandering around the forest at the same time that night. But, as I said, they arrived separately and each had their own indepedent means of knowing where Harry was.

We can be sure that Ron didn't know that Snape was there (since he's as clueless about who cast the doe Patronus as Harry is). But did Snape know that Ron was in the same forest seeking the same quarry?

He may have guessed that Ron was travelling with Harry and Hermione - I don't mean knowledge in that sense. I mean a knowledge that Ron was no longer in the tent with Harry and Hermione and was travelling around the forest on his own.

Did Snape know where Ron was, according to that definition? It would've been pretty awkward if they'd bumped into one another...

It is not explained anywhere in the book. I have just read that part again to confirm. See below:

And now Snape stood again in the headmaster’s study as Phineas
Nigellus came hurrying into his portrait.

“Headmaster! They are
camping in the Forest of Dean! The Mudblood-”

“Do not use that
word!”

“- the Granger girl, then, mentioned the place as she opened her bag
and I heard her!”

“Good. Very good!” cried the portrait of Dumbledore
behind the headmaster’s chair. “Now, Severus, the sword! Do not forget
that it must be taken under conditions of need and valor – and he must
not know that you give it! If Voldemort should read Harry’s mind and
see you acting for him-”

“I know,” said Snape curtly. He approached
the portrait of Dumbledore and pulled at its side. It swung forward,
revealing a hidden cavity behind it from which he took the sword of
Gryffindor. “And you still aren’t going to tell me why it’s so
important to give Potter the sword?” said Snape as he swung a
travelling cloak over his robes.

“No, I don’t think so,” said
Dumbledore’s portrait. “He will know what to do with it. And Severus,
be very careful, they may not take kindly to your appearance after
George Weasley’s mishap-”

Snape turned at the door. “Don’t worry,
Dumbledore,” he said coolly. “I have a plan...”

Now this is just a guess but I don't think Snape knew that Ron was wandering nearby when he went to Forest of Dean. He might have seen and heard Ron in the forest when he was already there but I don't think so. J.K. Rowling is sucker for details and something like knowing and then using that fact that Ron was nearby and would be able to help Harry out of the pond would be in the book.

On the other hand that just might be what happened and it was left as untold and for us to piece together.

Either way it is written nowhere in canon.

I think Snape was aware of Ron's presence. After all, Ron saw the Patronus and Harry following it which would mean he was close enough for Snape to notice.

Further, Snape would have arrived much earlier in the forest. He left Hogwarts when Phineas informed him. At that time, Harry and Hermione had just reached the forest. They setup wards, erected the tent, had dinner and turned in for the night before the appearance of the patronus. Snape would have waited and watched all the while to get Harry alone for the handover of the sword.

During his wait, being the powerful wizard he is, he would have identified any being, magical or otherwise around him - especially someone fumbling around like Ron would be. Snape would thus have actively avoided bumping into Ron.