How does one classify aqueous solutions of ions as acidic, basic and neutral?
Your approach thus far is correct. $\ce{Fe^3+}$ is acidic; $\ce{Fe(OH)3}$ is not a strong base. Indeed, if $\ce{Fe(OH)3}$ were a strong base, it would dissociate and form $\ce{Fe^3+}$, but, as you've mentioned, the opposite process happens.

Your confusion may arise from the fact that $\ce{Fe^3+}$ is a Lewis acid, and produces protons in a "different" way than Arrhenius acids:
\begin{align*} \ce{HCl &amp;&lt;=&gt; H+ + Cl-}\\ \ce{Fe^3+ + H2O &amp;&lt;=&gt; Fe(OH)^2+ + H+ }\end{align*}

Either way, your thought process (1.) will work for both cases.