HVZ reaction is given by only those carboxylic acids which have $\mathrm{\alpha }$ -H-atom. $\mathrm{C}{\mathrm{H}}_3\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}$ has three $\mathrm{\alpha }$ -H-atoms but formic acid does not have $\mathrm{\alpha }$ -H-atom hence formic acid cannot be halogenated.
For e.g. ${\text{CH}}_{\text{3}}\text{COOH}\text{+}{\text{Cl}}_{\text{2}}\underset{{\text{P}}_{\text{4}}}{\overset{\text{Δ}}{\to }}{\text{ClCH}}_{\text{2}}\text{COOH}\text{+}\text{HCl}$