There aren't any patterns, so you can't collapse any of those shapes into loops. You could remove the draw() function. When there is more than one shape of the same color at the same layer, you could set the fill once and draw all of the shapes.

Minor improvements:
- I used Ctrl+T to get spaces after commas, I find this more readable...
- I moved size() as first statement of setup(), as recommended.
- I used two constants to avoid repeating width/2 and height/2. BTW, good idea to parametrize your drawing like that.

Otherwise, you didn't made it wrong, it is also a good idea to comment like you did.
I thought also about reducing the number of fill() calls, but the order of drawing the shapes depends on the z-index (what is in front of other shapes).
Ah, you can also use constants for colors, thus no need for comments, and it helps in adjusting those in one place only.

1. void setup()
2. {
3.   size(600, 400);
4.   background(0, 150, 255);
5.  
6.   int hw = width / 2; // Half-width
   
7.   int hh = height / 2; // Half-height
   
8.   color WHITE = color(255);
9.   color BROWN = color(98, 23, 22);
10.  
11.   fill(WHITE);
12.   rect(hw, hh, 5, 100);//cow tail
13.   fill(BROWN);
14.   rect(hw+50, hh+40, 20, 100);//front left leg
15.   fill(WHITE);
16.   rect(hw+60, hh+50, 20, 100);//back left leg
17.   fill(BROWN);
18.   rect(hw-50, hh+40, 20, 100);//front right leg
19.   fill(WHITE);
20.   rect(hw-60, hh+50, 20, 100);//back right leg
21.   fill(BROWN);
22.   ellipse(hw, hh, 250, 150);//cow body
23.   fill(WHITE);
24.   ellipse(hw, hh, 100, 75);//cow head
25.   fill(BROWN);
26.   ellipse(hw-20, hh, 10, 7);//cow right eye
27.   fill(WHITE);
28.   ellipse(hw+20, hh, 10, 7);//cow left eye
29.   fill(BROWN);
30.   ellipse(hw, hh+10, 17, 7);//cow nose
31. }

PS.: I don't see two questions... And try a better subject line, like "How can I improve my code?" perhaps.