Lovers of Ahlul Bayt (AS) avoid celebrating or showing pleasure during the month of Muharram and Safar. That is because of the love and respect for Ahlul Bayt who suffered a lot in these two months.
Going on holiday is allowed as far as it does not include any sinful act like singing, dancing, listening to sinful music, keeping in mind avoiding celebrating or showing pleasure in these two months.
Wassalam.