I am making a buttercream covered cake, and was wondering if I need to refrigerate it or leave it on the counter. Also how do you cover it without messing up the finish. Or should I just make sure I cover with buttercream and fondant finishes the day of the delivery. Usually i just make them for home, but now I have to take it somewhere!!

Dont know about the buttercream, Im in the UK so its cooler here and I never need to put a cake in the fridge. As for covering the cake, you dont really need to just pop the whole thing in a box

I don't refrigerate my butter cream unless my cake is filled with a mousse filling with real whipping cream. My butter cream uses real butter and hi ratio shortening. The cream cheese butter cream recipe I use also doesn't require refrigeration.

I have not had luck refrigerating buttercream but I am wondering if it is because I live in such a warm humid climate. (I live near the ocean) I have tried to refrigerate a buttercream cakes, but when I take them out of the fridge, they sweat and get little beads of moisture on them. I have tried to refrigerate buttercream icing (wilton recipe) and if I let it come to room temperature to try to use it again, It sweats and breaks down.
I don't wrap my buttercream cakes, I place them in boxes.
If I keep my buttercream at room temperature, I have no problem with it. I also put my left over buttercream into the plastic tubs my shortening comes in and leave it out at room temperature. If it is for longer then 3 days, I usually pitch it, but I try to smell/taste to see if it is okay to use.
I hope this helps.

the buttercream I use I can leave out or put in fridge. I have a separate fridg for my cakes. I keep the temp not as cool as my regular fridg but cooler than setting out. Never a problem. Maybe you could turn your fridg temp up o it isn't so cold. I also freeze my buttercream if I have any left over. I have lots of little tubs of colored buttercream. That way I just let it defrost and I have buttercream ready to go. Never a problem.

As has been mentioned b'cream icing made w/even 1/2 butter and 1/2 solid shortening - even if you use a bit of milk to thin it - does not need refrigeration - either in keeping or on a cake.
It does not hurt to put it in the frig, but it is not needed.
If you do refrigerate it and it sweats when it comes out - just let it sit at room temp for about an hour and it should be just fine.
The beads of m;oisture will evaporate and not be noticed at all.
It is a good idea to but it in a cake box for storage - either in the frig or on the counter.
Storing in the frig or fzr is great. You can keep b'cream in the fzr up to a year. In the frig, about 2 months. On the counter about 3-5 days.

Thank you so much for all over your advise. I actually did a test cake and put it in the fridge overnight, took it out and it was like it started melting, frosting kind of slid down the cake causing cracks in my nice smooth finish. Will for sure not put the next one in the fridge!! Thanks again for the advise!
I will have to invest in some cake boxes, as I have none!

I never refrigerate my buttercream either.I use a few tsps of milk and i can still leave it out.