I know Granada used to do that back in the day. One of my drawings was featured in 1991! I think I have a VHS recording of it somewhere that my parents did. Don't know of any regions that still do that, apart from showing viewer photographs.
UTV have birthday announcements after the evening weather on UTV Live usually with photos of the child(ren). I know they used to have the puppets Busker & Barney read out birthdays earlier in the day but don't know if they still do that - I think the only other region announcing viewers birthdays is Channel TV with Oscar Puffin, but that's restricted to just weekends now.
I know BBC Spotlight used to show children's drawings in the Craig Rich era and I think David Braine continued this in his early days but they don't do this now, I think they occasionally have viewers weather related photos.