  We study the equivariant cobordism rings for the action of a torus $T$ on
smooth varieties over an algebraically closed field of characteristic zero. We
prove a theorem describing the rational $T$-equivariant cobordism rings of
smooth projective $G$-spherical varieties with the action of a maximal torus
$T$ of $G$. As an application, we obtain explicit presentations for the
rational equivariant cobordism rings of smooth projective horospherical
varieties of Picard number one.
