There were several asthmatic kids in my son's daycare and later in his Montessori preschool. The teachers were 100% familiar with the use of nebulizers and inhalers and could administer treatments. Of course, parents did their best to schedule the kids so they did not fall within daycare hours if possible. But everyone did their best.
My son occasionally needed an inhaler for several days after he got a cold. Although the pediatrician said we could use the albuterol 4 times a day for several days, he seriously only needed in 2-3 times a day for 1-2 days, if that. You will get accustomed to your son's patterns and chances are he may only need the rare treatment at school.
Sadly, asthma is an epidemic in this country. If all asthmatic kids missed school whenever they were on albuterol, they would never get to school. Also - we switched to an inhaler with spacer when DS was probably 3.5-4 (I am not sure exactly when). This was FANTASTIC. The inhaler takes 10 seconds, not the prolonged period of time the nebulizer takes. It is also silent and my son liked it much better (no sitting still for 10 minutes). He is now in 2nd grade. He has an inhaler kept in the nurse's office at school and if he needs it (never has during school), he can tell his teacher and go down there.
ETA -there are standard guidelines now for what constitutes good control, when a child needs to have further evaluation, when a child should be on steroids, etc. Talk with your pediatrician about what you can expect. For us, the winter is worse because the kids are all inside together, spreading colds around. Viruses are his primary trigger (cats too but they don't have those in school). So if he needs his inhaler for a couple of days, a month apart for several winter months, we don't worry. He will then generally be med free from April or so until Nov/Dec.
If you son has gotten sick monthly for a few months before he was diagnosed, that does not mean that interval will continue. Also - now that you know what you are dealing with, you will likely intervene before the horrible coupy/coughing/wheezing happens. More like when you notice the first cough.