I get that sometimes, though it started before I started riding, and isn't necessarily tied to exertion. The best guess I've encountered for mine is that it's some weird sort of asthma. I have an albuterol inhaler that I'll use sometimes if it's particularly bad.
That said, it seems to have gotten better overall with me commuting through the cold every day. I only have a problem now if I'm really huffing and puffing.