Is it a big deal if my 3 year old snores?

Possibly. When kids have allergies or colds it is not unusual for them to snore. However, if the snoring persists it may be a symptom of sleep apnea. This may happen when the adenoids enlarge and block air passage during sleep. Kids in this situation are restless sleepers, wake up frequently and they pause breathing for several seconds all during sleep. Sleep apnea affects development and must be evaluated.
Yes. The adenoidal/tonsillar mass will continue to grow faster than the kid until the age of 8 or 9 when it stabilizes. These narrow the airway and aggravate snoring. In my experience the kids who snore before 6 have a high frequency of sleep apnea/disturbance bith behavior changes and daytime sleepiness. Most need surgery to return to a more productive/normal life.
Depends. Light gentle snoring is not a big deal, heavy room shaking snoring or snoring that includes periods of apnea (stopping breathing) is a problem and needs to be evaluated by your child's pediatrician or ent.
M.D. visit. Airflow obstruction may cause the sound of snoring. There may be an area of the airway that narrows during sleep. Further testing is indicated if this occurs 4 or more times per week; if it is associated with behavior changes, poor growth or delay in achieving developmental milestones. Occasional snoring especially if it is associated with nasal congestion is usually not a serious condition.