What happens when ethanol is mixed with vinegar?

Probably nothing since vinegar is a dilute concentration of acetic acid...However if you had pure acetic acid & ethanol the two would react to form an ester called ethyl acetate at room temperature:

CH3CH2OH (ethanol) + CH3COOH (acetic acid) <==> CH3COOCH2CH3 (ethyl acetate) + H2O

However since it is an equilibrium reaction you'd have a mixture of the products & reactants & would need to separate the mixture. Under the presence of an acid catalyst (such as sulfuric acid) & continuously removing the water you can increase the yield of ethyl acetate.