The exchanging of presents among believers or the giving of
gifts to children is not an integral part of any of our nine Bahá'í Holy Days.
There is no prohibition against it, and it is, as you say, a custom among
Persian believers such as the Bahá'í to whom you spoke, to exchange gifts at
Naw-Ruz.
(From a letter written on behalf of the Universal House of Justice to
an individual believer, January 18, 1982; compilation: Lights of Guidance)