Here's a more straightforward "micro" plan. Essentially just a straight beeline towards their gold. We should be able to settle 1W of their gold on T51, unless that tile actually is ice in-game as well.
After all four workers have improved the sheep, one heads off to pasture the capital's pigs, wasting one turn in transit. It then builds cottages, or chops, or whatever. The pasture speeds the settler by one turn.
Another worker moves to the cow and pastures it, in time for Bloody Mary to work it at size two. It can then move 1E and chop, enabling Bloody Mary to complete an axe just as it grows to size three.
The remaining two workers simply move and road, starting from the sheep: SE -> NE -> SE -> NE -> NE -> NE (corn) -> NE -> NE (horses) -> NW (deer) -> NE (city site)
This feels relatively doable considering current unit placement. Their southeastern warrior shouldn't be a threat, and hopefully their western warrior will either stay put or keep exploring along the lake. If we can somehow juggle our axe over to escort the roading workers, the main threat would be an enemy chariot coming out of the fog. (That would be disastrous, though.)
If you know what I mean.