Should you put weight in the trunk of a small car for traction in winter?

No. This idea was used in early cars to weigh down the rear end of the car. This only worked when the majority of Cars were rear wheel drive.

Most modern cars, particularly small cars, are front wheel drive, and have the engine at the front. Having the engine over the front wheels pushes the front end of the car down, giving you all the traction you need.

Another disadvantage of adding weight to your car would be reduced economy of your car.

Also adding weight will increase the amount of distance required to stop the car. This would also make the car harder to control. Both of these factors would be multiplied by adverse weather conditions.

In summary, don't add unnecessary weight to your car at any time of the year.