Burning fields is illegal in some states.  It is allowed in other states and is usually regulated under a Smoke Management Plan.  Smoke exposure is a serious health concern and particulate matter pollution is regulated under the Clean Air Act.  

States that do allow field burning generally have times where burning is allowed, based on atmospheric ventilation and current vegetation moisture.  

 - If there is an atmospheric temperature inversion near the surface, or stagnant air characterized by no winds, then burning is not permitted.  
 - If the natural landscape is covered with dry fuels, burning will be limited so that there is no risk of the fire going wild. 

Some states regularly use pile burns (e.g. from timber slash, orchard tear-outs, mixed brush, etc.) so that the fire does not go wild and so that there is enough heat flux to allow the plume to break through a temperature inversion.