We compute the limit of the moments of the partition function $Z_{N}^{β_N} $ of the directed polymer in dimension $d=2$ in the subcritical regime, i.e. when the inverse temperature is scaled as $β_N \sim \hatβ \sqrt{\tfracπ{\log N}}$ for $\hatβ \in (0,1)$. In particular, we establish that for every $h \in \mathbb{R}$, $\lim_{N \to \infty } \mathbb{E}\big[\big(Z_{N}^{β_N}\big)^h\big]=\big(\frac{1}{1-\hatβ^2}\big)^{\frac{h(h-1)}{2}}.$ We also identify the limit of the moments of the averaged field $\tfrac{\sqrt{\log N}}{N} \sum_{x \in \mathbb{Z}^2} \varphi(\tfrac{x}{\sqrt{N}})\big(Z_{N}^{β_N}(x)-1 \big )$, for $\varphi \in C_c(\mathbb{R}^2)$, as those of a gaussian free field. As a byproduct, we identify the limiting probability distribution of the total pairwise collisions between $h$ independent, two dimensional random walks starting at the origin. In particular, we derive that $$ \fracπ{\log N}\sum_{1 \leq i<j\leq h} \mathsf{L}_N^{(i,j)}\xrightarrow[N \to \infty ]{(d)} Γ\big( \tfrac{h(h-1)}{2},1\big) \, ,$$ where ${\mathsf{L}}^{(i,j)}_N$ denotes the collision local time by time $N$ between copies $i,j$ and $Γ$ denotes the Gamma distribution. This generalises a classical result of Erdös-Taylor.