If its just a runny nose or a light cough, I would let them stay. If they have fever, are coughing constantly, sneezing constantly, I would send them home.
We attended a family birthday party for a 1 yr old once where my SIL called to say that my nephew was throwing up so they didn't know if they were coming. They took him to the dr. the dr. said it wasn't the flu. BIL called back to say they were coming. I asked them not to come because everyone else was already there, including a bunch of kids and the 1yr old whose party it was. MIL was just so upset that the nephew would have to miss the party and lets let him come anyway. I said, my kids are already here having a good time, but if you let him come I'm taking my kids home. Oh but he'll be so sad that he missed the party, I say he's coming, and he did, and as soon as he walked in the door, me and my two kids walked out.
3 kids from that party ended up getting sick 2 days later. Including the daughter of the host.