I noticed that the question came up in Zenit’s weekly liturgy Q&A column. Fr McNamara’s assessment, after quoting the relevant documents:
Therefore, there is no universal rule that would forbid the practice of baptism during Lent. However, given that Lent is traditionally orientated toward the preparation for baptism, many parishes and even a few dioceses have policies that discourage it.
Another reason why several places discourage baptisms during Lent is that in some cultures they also give rise to festive social celebrations that might be inappropriate during a penitential season.
Since these regulations forbidding baptism during Lent are never absolute, pastors always retain the possibility of setting them aside for a good reason and so decide to perform a baptism.
This has been my experience: baptisms are discouraged, but exceptions for serious reasons are permitted. It’s pretty much the same for weddings. I recently consulted with a couple getting married in another parish–their wedding was last weekend. There is no rule against a Lenten wedding, but many couples would blanch at the thought of toning down a celebration in keeping with the spirit of the season of Lent.
Anybody getting married or baptized at your parish this Lent?
Catholic Sensibility 
My wife and I waited until the first Saturday after the Easter octave for our EF wedding. My son was born the next year early in Lent and baptized the following week in the older form. How’s that for consistency? I doubt the priest for our wedding would have offered the nuptial mass in Lent and suspect that the priest who baptized our son would’ve thought us crazy to delay baptism until the end of Lent. From what I gather, it seems like the opposite sequence is more common (wedding in Lent and baptism after, not baptism of child with wedding of parents later!)
I work at one parish and worship at another. Where I worship, there seem to be baptisms and weddings during Lent.
Where I work however, no baptism during Lent and I can tell you, many people call seeking baptism for their infant. I try to be as pastoral as I can but sometimes they demand to speak to our pastor. Who basically tells them what I did… *sigh*
As for weddings we had one during Lent this year. The couple was intent on it but it was very toned down, few flowers for example, which I think made the bride unhappy.
I think it’s outrageous to postpone an infant’s baptism due to the season.
Canon 857: “…[p]arents are obliged to take care that infants are baptized in the first few weeks.”
Ok, let’s quibble over “few”, but it would seem exceedingly un-pastoral for a priest to not baptize an infant as soon after birth as the parents request it.
Laetare Sunday, St Joseph’s Day and Annunciation would be good days to choose for Lenten baptisms, given their festal character. Laetare in particular should help eliminate quibbling over “few weeks”.
In 1961, I was baptized on St Joseph’s Day, some 4.5 weeks after I was born. And my siblings were generally baptized a month after birth, and that was the common pattern. Moreover, my mother and I nearly died in labor, and were in the hospital for more than a week after birth, but that was not considered sufficient reason to accelerate my baptism even in those days.
Hello! I am going through the RCIA process this year and my husband was raised Catholic. We were married six years ago and the Church has asked that we marry in a Sacramental ceremony prior to Holy Week as I will be baptized. Thus, it seems important despite the Lenten season. In fact, as part of Scrutinies of Lent it is in reconciliation. A small ceremony and no after celebration.