No, a steward was not a peasant.
Contrary to what is often stated, there was always a middle class in the Middle Ages, and stewards were members of the middle class. They were the equivalent of Accountants or managers, and were educated, so they could keep notes and take care of bookkeeping.
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The steward did not usually organize events. His job was managing the possessions of a wealthy person, nobleman, or possibly a kingdom. Please see the related question, "What job did a medieval steward have?" There is a link below.
A peasant
The gamekeeper would have been in the peasant class.
The medieval soap maker was considered a serf or a peasant.
Many medieval women had maids. Even the wealthier peasant families had servants in some times and places.