  Cool gaseous exoplanets ($1.75\ R_\oplus < R_\text{p} < 3\ R_\text{J}$, $200$
K $<T_\text{eq} < 1000$~K) are an as-yet understudied population, with great
potential to expand our understanding of planetary atmospheres and formation
mechanisms. In this paper, we outline the basis for a homogeneous survey of
cool gaseous planets with Twinkle, a 0.45-m diameter space telescope with
simultaneous spectral coverage from 0.5-4.5~$\mu$m, set to launch in 2025. We
find that Twinkle has the potential to characterise the atmospheres of 36 known
cool gaseous exoplanets (11~sub-Neptunian, 11~Neptunian, 14~Jovian) at an SNR
$\geq$ 5 during its 3-year primary mission, with the capability of detecting
most major molecules predicted by equilibrium chemistry to > $5\sigma$
significance. We find that an injected mass-metallicity trend is
well-recovered, demonstrating Twinkle's ability to elucidate this fundamental
relationship into cool regime. We also find Twinkle will be able to detect
cloud layers at 3$\sigma$ or greater in all cool gaseous planets for clouds at
$\leq$ 10 Pa pressure level, but will be insensitive to clouds deeper than
$10^4$ Pa in all cases. With these results we demonstrate the capability of the
Twinkle mission to greatly expand the current knowledge of cool gaseous
planets, enabling key insights and constraints to be obtained for this
poorly-charted region of exoplanet parameter space.
