5 yr old daughter has hives on face and lots of mucous in lungs just on the walk to school, what could it be?

Allergy?: Hard to give a definitive answer by your description..."mucous in lungs" is horrible sounding(i presume you meant a phlegmy cough); and just from walking to school sounds like an environmental allergy. If this is not the case then i recommend a trip to your friendly neighborhood pediatrician for a thorough exam for your 5 year old.

Atopic state: Seems unfair but children & adults who have one kind of allergic illness, often have several including asthma, allergic rhinitis & conjunctivitis, eczema, hives, anaphylaxis, & a recently identified problem involving swallowing called eosinophilic esophagitis. Your daughter could have both asthma & hives, possibly triggered by cold air. Start solving this mystery be visiting her pediatrician soon.

Non-allergic...: Etiologies could cause both conditions. This is called cholinergic urticaria in conjunction with cholinergic rhinitis which could be causing post-nasal drainage. Regardless, she needs to be evaluated by a physician in the near future to better determine the etiology of her symptoms.