Hundreds of drivers have been caught speeding in the New Forest in the past two years, Forestry England has revealed.
The organisation also says only one in four of those stopped by police knew what to do if they hit any of the area's free-roaming animals.
Now motorists are being told to "expect the unexpected" ahead of the deadliest time of the year for animal accidents.
A large number of collisions occur in November and December, when the weather and light conditions are notoriously unpredictable.
A Forestry England spokesperson said: "Several hundred drivers have been caught speeding over the last two years by Operation Mountie, a multi-agency road safety project led by Hampshire police.
"Speeding motorists were stopped and either given tickets or education.
"Despite it being a legal requirement to report an accident involving Forest animals to the police as soon as possible, and within 24 hours, only 26 per cent of motorists stopped were aware of this."
Gilly Jones, of New Forest Roads Awareness, added: "Animals roaming across the Forest have right of way and can be extremely unpredictable.
"Drivers need to be able to react quickly and if the worst does happen it’s essential they know what to do.
"If you're involved in an accident with a Forest animal, please call 999 immediately even if it runs off as it may have an internal injury."
Charlotte Belcher, community manager for Forestry England, said: "As the light fades and the weather starts to become more unpredictable all of us travelling through the Forest need to take extra care.
"Many of those we speak to are aware of the risks but think it won’t happen to them. It’s not worth taking that risk."
Sue Westwood, clerk to the New Forest Verderers, added: "Please pass wide and slow when approaching ponies and other animals.
"This is especially important during the autumn and winter months when it's dark, foggy or raining or you are blinded by oncoming headlights or a low sun. Expect the animals to walk out in front of you, they have no road sense.”
Police-led operations to combat speeding will continue in the coming months.
Sergeant Robin Blake, of the New Forest Heart Neighbourhood Policing Team, said: "Incidents can cause major harm and distress to animals, their owners, and the drivers involved.
"It's really important to be aware that driving conditions throughout the year change and can have a significant impact on Forest roads."
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