These were growing on a good-sized bush in a back yard near the east end of the park. I'm not sure what it is yet.

UPDATE: This is a Lady Banks Rose (Rosa banksia). I have photos somewhere of the whole bush, which is large and starting into a tree, but still a bit small in comparison to photos I've seen of other examples. Whether this is due to weather damage, pruning years ago (it's in a neglected part of a backyard and doesn't appear to have had much attention in recent years), or the fact that it may just not be all that old, I don't presume to say.

Several of my sources insist that the White Lady Banks has a strong fragrance reminescent of violets, but I couldn't detect any scent from this plant. Fragrance in roses is apparently highly variable depending on climate, soil conditions, time of day, the nose of the sniffer, etc., so it may actually have a nice scent normally - I'm just not able to pick it up.

Here's a page with more info at helpmefind.com:
http://www.helpmefind.com/rose/l.php?i=A6458&tab=1

At least one user apparently uploaded some photos of the yellow variety by mistake, so if the page loads with a photo of a yellow rose, don't think you have the wrong web page.

TRIVIA: A rose of this type growing in Tombstone, Arizona currently holds the record for the world's largest rose plant. There are several websites that mention this and/or have photos - the following page is only one example:

http://www.goldcoastrose.org/shared/tombstone.htm