For it to have "little children [to be] born and live and die all in darkness" then the planet would be in darkness for ~20 years; if this is regular event then most life would die.
If you are after severe planet wide winters, during which the planet cools dramatically, with the sun shrinking in the sky, howling winds, seas of ice growing from the north and the south, then a planet with a more eccentric orbit would would work (the images show orbits with different eccentricities, earth is ~$0.02$).
On the part of the orbit where it is further from the sun the planet, would receive less sun light an cool down, as such it would be planet wide phenomenon, also at the planet is further away from the sun, the sun would be smaller in the sky (not necessarily by much). Depending on how eccentric the orbit is, the effects could range from a global winter. All the way to when $e$ is close to $1$, when for most of the year the planet is far from the sun, and it is a frozen ball of ice, where even the atmosphere may start to condense (ie raining liquid nitrogen/oxygen), where the sun is a small dot in the sky.
hopefully that helps
