The Chasam sofer in his commentary to Maseches Shabbos, writes that although the Gemara clearly states that women are obligated to light נר חנוכה, but due to modesty concerns כל כבודה בת מלך פנימה (because the primary תקנה was to light candles out on the streets), women do not light and they are יוצא with their spouse's Mitzva.
Question 1. Do we find any other commandment's that women are exempt from, due to צניעות?
Question 2. Just like we find in the Gemara at the end of Maseches Tannis that women use to take to the streets and mingle with the men on Tu Baav, and try to find for themselves spouse's to marry. Then obviously for Mitzva purpose's we do forgo some modesty restrictions, then why would נר חנוכה be any different?