Q. I reside in a city without an eruv and I just acquired a small dog for company, and I have a few shailos.
Can I take out the dog on Shabbos to the street with a leash and wearing his tags on a collar that I don't usually take off?
A. It is a Biblical requirement (Shemos 20:10) to have the animals one owns rest on Shabbos and Yom Tov. This implies that the animal avoids any activity prohibited for the owner to perform on these days, unless such activity is done for the benefit of the animal. Therefore, it is forbidden if the animal is wearing an object from which it derives no benefit, to enter an area in which the owner is forbidden to carry. Shulchan Aruch (O. C. 305: 1) rules that decorative items should not be worn by an animal when its owner takes it into an area not enclosed by an eruv since an animal does not benefit from such items. Shulchan Aruch (O.H. 305: 1, 16) rules that an animal can be walked on a public domain while being held by a leash. However, one should make sure to hold it in a way that the leash does not hang out more than a tefach (10 cm.) from his hand.
In regard to the dog tags on the collar, depends mainly on whether the tags are considered a benefit for the dog or for its owner. Aruch Hashulchan (305: 5), Shemiras Shabbos Kehilchoso (27: 9) and others rule stringently, even though nowadays law requires that dogs wear tags and it can save the animal from being seized by others or impounded by authorities and even being put down.
However, Shemiras Shabbos Kehilchoso (27: 9: n. 33) quotes that Horav S.Z. Auerbach zt'l was lenient. He argued, that although tags are not a natural benefit to the animal, only man dictated, still it should be considered a benefit to the dog, and permitted. (He also alludes that if the tags are very well attached, in a way that it is difficult to remove them, one may be lenient).
Chashukei Chemed (Shabbos 52a) debates if an animal is allowed to go out on Shabbos wearing a light reflective band, so it will be seen and not be hit by cars at night. He leans to be lenient, since it could be considered a tachshit for the animal if it always wears it.
Rabbi A. Bartfeld as advised by Horav Shlomo Miller Shlit'a.