The Counting of the Omer
8. The "sundik" (the person who holds the baby during a circumcision), the
"mohel" (person performing the circumcision), and the father of the baby
may cut their hair (and shave), [even] on the day before a bris
(circumcision) toward evening (1), shortly before they go to the synagogue
[for the afternoon serivce] (2).
9. [A couple] is permitted to become engaged (3) and even to hold a
special celebratory meal ("seudas mitzvah"), at any time during the days of
counting the Omer. Dancing, however, is prohibited.
(1) And, of course, on the day of the bris itself, which is considered like
a Yom Tov for these three individuals.
(2) If the circumcision will be held on Shabbos, one is permitted to take a
haircut or shave on Friday, even before midday.
(3) This is permitted because there is a fear that if one put off one's
engagement, someone else might propose in the interim (Mishna Berura 493:3).