Frost Damaged Rose Stem?

I spotted this dying rose stem (the one on the right) on one plant whilst applying feed. Don't think it was there before when I applied fungicide, though not certain. Definitely looks like the start of something, probably dieback. Although, having said this, on first impressions I would say it was a burn of some sort - perhaps caused by the spray or, more likely, by frost.

IS IT TOO MUCH FEED?
Last year I gave rather a lot of feed: A lot for me, that is. I only gave the recommended dose. But this could have caused new growth to continue too late into the autumn, with insufficient ripening taking place. Lots of soft green tissue is asking for trouble where frost is concerned.

Of course, it might not be frost damage. But it IS the coldest plant. And it's the only one affected in this way. Were the damage caused by spraying, other plants would have been damaged.

TREATMENT
I used same feed as last year but cut rate in half. Back to normal.