Yes, but...meat was only plentiful for the rich/royalty/elites.  The typical citizen/peasant didn't have meat often.  1) They didn't own the land or the animals.  2) It wasn't their meat; they just worked the fields.  3) You still didn't have meat 'year round' like in our modern times. 

Cows, pigs, sheep give birth in the spring, they grow and you slaughter them in the fall.  Then you ate meat and fatty foods in the winter, because you wanted to gain weight for the cold weather.  In the spring/summer months, you were out working the fields and you ate what nature gave you -- fruits, grains, etc.  Plus, in hot weather, you don't want to eat a lot of oily foods - it makes you sluggish. 

The famous 'London Tower' guards known as the 'beefeaters'.  They were given as much meat to eat as they wanted; it was a perk of their job.  They were known as 'beefeaters' precisely because MOST normal, avg joes could not eat as much meat as they wanted.  It just wasn't available.

History shows that many kings/elites died of "gluttonous" medical conditions (i.e. diabetes, heart issues, etc).  The avg citizen didn't have these conditions.

p.s. The olden Fasting laws of the Church would've had catholics fast from meat about 1/3 of the year.  The current Orthodox fasting laws have about a 120 days of fasting per year.  That's a LOT of days without meat.