Daycare CANNOT exclude for common colds. Do not let them! It's not within the "Staying Healthy in Childcare" guidelines.
As Tobily said, no fever, eating, drinking OK etc, it's no worries. Jury's out on the whole clear/yellow/green snot thing anyway. Some doctors say yellow/green is the expulsion of the infection, others say that's when they're contagious, some say it depends ont he individual. We had a little one at a daycare where I worked who had green snot for 10 weeks. And it was only 10 weeks because we stopped counting after that! And she was fine the whole time, just a really uniquely snotty kid.

at drop-off, just explain that the child has had a runny nose, but has otherwise been OK, and that you'll call in a few hours to see how they're going (much nicer than asking CCWs to call you - it's far easier to be handed a phone than to leave 10 babies behind and search out the phone, find your number in a file of 46 children then call your work number, mobile, then partner's number as well because nobody's answering)

That's what I would do, and that's what I would love most parents to do
i hope it went OK.