A number of songs are put into the pile with "Martin Said to His Man," in which animals perform unlikely activities. See The Traditional Ballad Index. Included are Kitty Alone, Johnny Fool, Hurrah, Lie!, The Bed-time Song, Who's the Fool Now?, Old Blind Drunk John, and Fooba-Wooba John. The earliest date is 1609 for "Martin Said To His Man" (but registered in 1588).

"I saw a crow flying low," mentioned by Joe Offer, Matt S. and Dicho, appears in "Johnny Fool," Randolph vol. 3, pp. 200-201. A few verses:

I saw a crow flying low,
Hooey, hooey, hooey, hooey,
I saw a crow flying low,
Hooey, hooey, John.
I saw a crow flying low,
It was eight miles under snow,
It was the last time
For old blind Joe

I saw a louse chase a mouse, etc.
From the kitchen to the house, etc.

I saw a sow weaving silk, etc.
And her pigs were stripping milk, etc.,

I saw a flea wade the sea, etc.
And it struck him to the knee, etc.

Also, in another variant:
I saw a sow weavin' silk,
While six pigs was churnin' milk,
Johnny Fool, Johnny Fool.

Saw two geese makin' cheese,
One would hold and the other would squeeze, etc.

Saw a mule teachin' school,
To the bullfrogs in the pool, etc.

These songs seem to depart pretty far from the "Kitty Alone" group.
I couldn't find lyrics for "Martin Said To His Man."