Startups tend to be less picky about year of graduation and more interested in the capabilities of the student. The best intern I've had was a sophomore who within a month was contributing like a regular member of the team. We had him stay on part-time through the next school year.
I'm pretty confident we'll find good students again this year even in April. If this experiment goes well, we'll probably try another push in the fall to help startups edge in on big company recruiting territory.
I'd hesitate to stereotype startups' hiring preferences, but encourage students to apply to any company that's remotely interesting. Just like the bigger corporations, there's a huge variance: I've approached some startups about internships only to realize that their singular focus was to bring on full-time engineers ASAP, and worked for others that hired and mentored younger students with great success. It's often impossible to tell without starting a conversation.