Like the others above, I don’t think there is an actual written rule against it. Our parish, which is the diocese cathedral basilica, used to not permit weddings during Lent or Advent, but when a new pastor came, he opened Lent and Advent for weddings. So, it has stayed that way with the subsequent pastors after him.
I do know that some parishes still do not permit it, but it appears to be more on an individual parish level - at least in the dioceses that I’ve worked in as a musician. They are not as often as late spring through fall weddings, but I have found that if a parish does permit it, there will be many weddings during Lent - especially now with the economy and discounts offered by wedding vendors usually around the early part of Lent. The couples that are getting married around Lent tend to be also the couples who are not throwing large or extravagent receptions.
For the OP’s particular situation, it’s best to ask the pastor of the parish.