You must act. You cannot allow a dog to stay outside without adequate shelter. 

Outdoor Shelter

3.2-6503

Every companion animal (including dogs) must have adequate shelter. Failure to provide adequate shelter is a Class 4 misdemeanor

3.2-6500 

Adequate shelter, such as a dog house, in the cold weather must:

• Protect each animal from injury, rain, sleet, snow and hail

• Protect the animal from the adverse effects of the cold

• Has a windbreak at its entrance

• Provides a quantity of bedding material consisting of straw/hay, cedar shavings or the equivalent

• Be clean and dry

There are more requirements for shelter under 3.2-6500, but these are the primary factors to consider in cold weather. 

Under 3.2-6569, a dog can be seized if there is an apparent violation of any provision of Chapter 65. 

Outdoor Tethering

3.2-6500

Outdoor tethering of an animal is prohibited under the following circumstances:

• When the actual or effective outdoor temperature is 32 degrees Fahrenheit or lower.

• During the effective period for a severe weather warning issued for the area by the National Weather Service, such as a winter storm.

An exception can only be given if the animal control officer properly inspected the animal’s individual circumstances and can guarantee that the animal is safe from predators and well suited and well equipped to tolerate its environment.

The length of the dog’s tether is regulated too. Adequate space means that the tether must:

• Be at least 15 feet in length or four times the length of the animal, as measured from the tip of its nose to the base of its tail, whichever is greater.

• Not get entangled with other objects or animals or extend over an edge.

• Not weigh more than one-tenth of the animal’s body weight.

An exception can only be given if the animal control officer has properly inspected the animal’s individual circumstances. Then the tether can be 10 feet or three times the length of the animal.

Under 3.2-6569, dogs can be seized if there is an apparent violation of any provision of Chapter 65. 

The full definitions of adequate shelter and adequate space can be found here: § 3.2-6500. Definitions.