The closure of GP practices and some NHS services over Christmas led to an increase in 999 calls for seasonal illness and falls on icy pavements.
And hazardous driving conditions have led to Yorkshire Ambulance Service crews taking longer to reach patients in some areas.
People calling the non-emergency 111 number, which is operated by the ambulance service, have also seen delays getting their calls answered.
Yorkshire Ambulance Service said it was seeing rising demand on its crews even before the icy conditions and freezing temperatures started.
Dr David Macklin, executive director of operations, said: “We don’t want to deter people from calling 999 in serious cases such as heart attack, breathing difficulties or stroke for example and please be reassured that we are focusing our efforts on reaching patients with life-threatening illnesses and serious injuries as a priority.”
The ambulance service had already issued a plea for people to use the service wisely after the weekend of December 12 was its busiest ever for dealing with seriously-ill and injured patients.
Mid Yorkshire Hospitals Trust has also seen hundreds more patients attend its A&E departments compared to the same time last year.
People are advised to ring the NHS 111 number to help ease pressure on A&Es, but that service is also struggling to cope with demand.
Dr Macklin said: “Our NHS 111 service is also under pressure and we are asking everyone to be patient as it is taking longer than usual for calls to be answered and for our clinical staff to ring callers back.”