Allah has mentioned in the Exalted Quraan : '...And you (the wives of Nabi SAW) should adhere to your houses...' (Surah Al-Ahzab, verse 33)
Rasulullah SAW has said in a hadith : It is not permissible for a woman to undertake a journey (of 88 km or more) without a mahram (one whom she can never marry eg. father, brother, uncle etc.)
Therefore, it is understood that women are not permitted to travel without a mahram. However, if you really want to go ice skating, then instead of your friends, ask your parents to go with you and spend some quality time together. In this manner, your relationship between your parents could become closer too insha Allah. The reason why Shariah has allocated a mahram to accompany a woman is so that she will always remain protected and no harm may afflict her as a Muslim woman is something precious and should always be protected.