Are Cuts and Abrasions an Emergency?
Minor wounds, cuts, and abrasions are the kind of scenario where common sense should rule.
You wouldn’t rush your kid to an emergency with a scraped knee, and you don’t need to do that with your dog either. But …
Abrasions
An abrasion is a wound caused by superficial damage to the skin …
wikipedia

Abrasions further break down into three grades ranging from scrapes/grazes to avulsions. An avulsion refers to a surface trauma where all the layers of the skin have been torn away, exposing the underlying tissues. In other words, an abrasion can be a mild injury or a substantial trauma.
While superficial skin damage is not an emergency, skin ripped away and revealing muscles, tendons or bone would be.
Not because it is in itself life-threatening but being taken care of properly is imperative.
This would be particularly true if a dog suffered an avulsion as a result of falling off or out of the vehicle, or other, similar scenarios where further, more serious injuries are possible even though not readily apparent.
Always an emergency in the following cases
Jumping or falling out of a vehicle, being in a car accident, falling off heights, etc. are always an emergency regardless of how minor the injuries might look.
It should indeed be common sense to evaluate the injuries as you can see them as well as what led up to them.
I’d like to note that chronic injuries to feet and foot pads, while not an emergency, should be evaluated. Foot pads can suffer from chronic exposure to hard, abrasive, or hot surfaces, the tops of the feet might keep being injured from neurological deficits.
Cuts, lacerations, and puncture wounds
Similar distinctions need to be made when it comes to cuts, lacerations or puncture wounds.
- how did the injury happen?
- what is the amount of bleeding?
- how deep is the wound?
- could there be foreign matter left in the wound?
It is quite easy to underestimate how deep a cut might be.
There is also a limited window during which such a wound can be expertly sutured or glued. Many veterinarians recommend having all cuts seen and tended to.
It’s also important to keep in mind that the odds of such wound getting infected are high.
With cuts and abrasions, use good sense. It is better to overestimate the potential damage than the alternative.
Related articles:
Canine Wound Care 101: Classification, treatment, and physical therapy
Further reading:
How to Treat Dog Wounds at Home
Cuts and Bruises on Dogs