I don't "save" separately for holidays but I do budget for them, if that makes sense.
It's probably a bit OTT but I have a budget spreadsheet for both myself and wife and we update them at least twice a year to reflect our expected income and expenditure by month on a rolling 18 month basis. (I don't update it retrospectively for actual spend - it just gives us a plan for the year)
One of the most important lines in the expenditure section is the holidays line. I include the approx cost of the holiday (including parking, cattery etc) in the months that we'll have the money going out (deposit on booking, balance 2 months before, cattery and spending money on return, etc), I reduce our food and petrol costs in the budget for the months in which we will be away.
This means that I know we can afford the holidays before I book them and if money looks tight I budget for cheaper holidays rather than 'overspend' and end up borrowing.