And today nosegay makes it sound as if only a person's nose is gay.  Since many people might react to the gay portion of the word as having to do with a person's sexual orientation, I doubt this term will be used very often in the present day.  

Shakespeare used this term in his play to mean flowers that were pinned to the garments a person was wearing, such as a corsage or a multiflowered boutonniere.  I'm not sure if this was thought to disguise body odor or to disguise the general smell in the area for the person wearing the flowers, because Medieval cities were filled with a variety of disgusting smells. 

You might have also heard the following nursery rhyme: as a child 
Ring Around the Rosie 
Pockets Full of Posies 
Ashes, Ashes
We All Fall Down 

This nursery rhyme was about the Bubonic Plague or Black Death.  The 'Ring Around the Rosie' referred to the red ring that first formed, and then it turned into a black boil.   'Pockets Full of Posies' is because at the time people thought diseases, such as this. were spread by smells, so the kept pockets full of fresh flowers to keep from getting the disease.   Doctors at the time would wear masks with long beaks that were filled with flowers or other strong smells when treating patients.  'Ashes, Ashes' refers to burning the dead bodies, and 'We All Fall Down' refers to the huge number of people that contracted the disease. 

So nosegay were very important to people during the Middle Ages. 

I have been to my fair share of weddings, but 'a nosegay' is a new one on me. I think 'a bouquet' will remain my first thought, in the time I have left.

Quote

Brides typically carry a nosegay up the aisle.

As so often happens, when I look up one of the 'Words of the Day' other tidbits come to light.

Nosegay - Wikipedia

(A nosegay, posy, or tussie-mussie is a small flower bouquet, typically given as a gift.)

The term tussie-mussie (also tussy-mussy) comes from the reign of Queen Victoria (1837–1901), when the small bouquets became a popular fashion accessory. Typically, tussie-mussies include floral symbolism from the language of flowers, and therefore may be used to send a message to the recipient.^[5] In modern times the term specifically refers to small bouquets in a conical metal holder, or the holder itself, particularly when used at a white wedding.

Tussie-Mussies Popular Victorian Fashion Accessory - Antique Trader

@sandrewn wrote: 

I have been to my fair share of weddings, but 'a nosegay' is a new one on me. I think 'a bouquet' will remain my first thought, in the time I have left.

Brides typically carry a nosegay up the aisle.

The term tussie-mussie (also tussy-mussy) comes from the reign of Queen Victoria (1837–1901), when the small bouquets became a popular fashion accessory. Typically, tussie-mussies include floral symbolism from the language of flowers, and therefore may be used to send a message to the recipient.^[5] In modern times the term specifically refers to small bouquets in a conical metal holder, or the holder itself, particularly when used at a white wedding. 

So I assume a collection of black or dead flowers meant 'you're on my hit list'.