Plans submitted to East Riding Council for the park, off Long Lane between Beverley and Woodmansey, stated it would help to meet demand for walking spaces in short supply locally.
Documents from the applicants stated it would come ahead of new homes due to be built in the area and after pet purchases rose during the coronavirus pandemic.
But three objections have been lodged against the plans over noise from barking dogs disturbing residents and horses and its impact on the right of way to a neighbouring home.
Plans for the site, currently a grazing field, would see the park cover an area of around 13,911sqm if approved.
A 1.8m high fence would be built around its boundary, fitted with deer and rabbit mesh and sunk to stop dogs digging under it.
It would have six parking spaces and plans stated it would be in an “ideal” location close to Beverley, Woodmansey, Dunswell, Cottingham and north Hull.
They also stated its location off Long Lane would provide a “safe” option for those using the road to walk dogs currently.
The plans stated: “The increase in new housing alone will naturally bring more pets to the area and the need for dog walking facilities will benefit an already under-resourced sector.
“People owning dogs has also risen greatly through lockdowns caused by the coronavirus pandemic, with people looking for activities they can enjoy locally and the company a new pet can offer.
“The requirement for enclosed areas for dog training of new pets and those that have been re-homed following abuse also emphasises the need for such facilities providing safe and secure environments for owners to train their dogs.”
Two comments supporting the application have been submitted, stating it would stop dog walkers trespassing on private land which is currently an issue for locals.
But one of the three objectors claimed it would see more people going onto a private footpath without permission and cause “anxiety and stress” for their horses.
The objector stated: “We strongly oppose this and this will cause upset to not only us as residents but also the animals that we have at home.
“Horses do not respond well to unfamiliar dogs and are flight animals. Such noise will cause unnecessary stress to our horses which could result in their injury.
"We also have dogs which will be set off barking and being territorial when they can hear stranger dogs across our driveway. This is too close to our properties to not be a distraction.”