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Let $X$ be a 3-dimensional affine variety with a faithful action of a2-dimensional torus $T$. Then the space of first order infinitesimaldeformations $T^1(X)$ is graded by the characters of $T$, and the zeroth gradedcomponent $T^1(X)_0$ consists of all equivariant first order (infinitesimal)deformations.  Suppose that using the construction of such varieties from [1], one canobtain $X$ from a proper polyhedral divisor $\mathscr D$ on $\mathbb P^1$ suchthat the tail cone of (any of) the used polyhedra is pointed andfull-dimensional, and all vertices of all polyhedra are lattice points. Then wecompute $\dim T^1(X)_0$ and find a formally versal equivariant deformation of$X$. We also establish a connection between our formula for $\dim T^1(X)_0$ andknown formulas for the dimensions of the graded components of $T^1$ of toricvarieties.

Equivariant deformations of algebraic varieties with an action of an algebraic torus of complexity 1