The Glasgow-based travel company, which employs about 850 people, highlighted particular buoyancy in its long-haul business.
The company said yesterday that its sales of long-haul leisure travel in the period between January 1 and March 31 were up by 40 per cent on the same period of last year.
Founder, chairman and minority shareholder Bill Munro cited strong demand for holidays to the US state of Florida and the Caribbean. Mr Munro, whose daughter Sharon is now majority owner of Barrhead Travel, highlighted an increased focus by the company on long-haul business because this segment of the leisure travel market was viewed as having particularly strong growth potential.
Barrhead Travel also cited strong year-on-year growth in first-quarter bookings for cruises.
The Met Office said at the end of February that Scotland had experienced its wettest winter since comparable records began in 1910.
Sharon Munro, chief executive of Barrhead Travel, said: "Scottish holidaymakers have been flocking in their droves to book a summer getaway following the poor weather over the winter months.
"January to March is always a busy time for us. However, this year we've enjoyed an exceptional response from travellers looking to jet off to foreign shores."
Mr Munro meanwhile noted that 46% of Barrhead Travel's revenues now came from outwith Scotland, mainly England.
He said of this business from outside Scotland: "That has kept Scottish people in a job."
Asked if he believed the rise in bookings was because there was more money around, Mr Munro gave his view that there had not been a big increase in households' disposable incomes but he believed people were more confident and therefore more willing to spend.
Mr Munro believed people were generally a lot more secure in their jobs.
He added: "I don't think there is a huge amount more disposable income available.
"I think the confidence is coming back and that is encouraging people to spend what they have got."
Mr Munro cited the benefits of new direct flights from Scottish airports. He highlighted flights from Edinburgh Airport to Doha in Qatar and to Chicago in the US.
He added that Chicago was a great city for a weekend break.
He also cited demand for river cruises, in Europe and destinations further afield, including the Mekong Delta in Vietnam.
Mr Munro said Barrhead Travel's sales of holidays to Canada were growing every year.
Commenting on Barrhead Travel's traditional package holiday business, and citing competition from budget airlines in this arena, he added: "The sand, sea and sun (business) is remaining steady. We are not seeing big growth in that marketplace, probably because you have all the no-frills chaps in there."