It is indeed possible that in the early Solar System, before the short-lived radioactive elements completely decayed, there were some asteroids with good conditions for the appearance of life.

However, I would not describe those as small. The majority of the interplanetary bodies that orbit the Sun and which fall from time to time on Earth as meteorites are far too small to have ever had conditions for the appearance of life.

Even an asteroid like that which has wiped out the dinosaurs, with a diameter of a few km could not ever have suitable conditions.

Only relatively large asteroids, presumably with diameters from tens of km to hundreds of km, might have had warm interiors and volcanism for enough time to allow the appearance of life.

Such asteroids must also have been among those distant from the Sun, in order to contain enough water and volatile chemical elements.

The fact that the most volatile chemical elements are those most important for life is not due to chance, but due to the necessity. The volatile elements are those prone to forming covalent chemical bonds. Unlike the metallic or the ionic chemical bonds, the covalent bonds are strictly required for forming the complex molecular structures that may lead to living beings.