Kids have such soft, silky, sensitive skin.  I don't think any tissue can prevent a red, chafed nose when they get a bad cold.  I've tried coating the area with lotion, which feels like the skin is burning, and I have tried white petrolatum jelly and neither work well. 

I have found that Aquaphor works great.  It doesn't burn, it protects, and it heals.  I saw a dramatic improvement in the morning when I put some on my son's nose before he went to bed the night before.