From 10:15 a.m. to 3:30 p.m. $= 5$ hours $15$ minutes $= 5\frac{1}{4}$ hours.

$\text{Snow} = 5\frac{1}{4} \times \frac{1}{2} = \frac{21}{4} \times \frac{1}{2} = \frac{21}{8} = 2\frac{5}{8} \text{ inches}$