Does the LDS discuss the issue of LDS children "playing Sacrament"? In the LDS faith, the Sacrament (most analogous to the Eucharist in other Christian faiths) is a very sacred ordinance performed weekly as part of Sacrament Meeting:


  Partaking of the sacrament is a witness to God that the remembrance of
  His Son will extend beyond the short time of that sacred ordinance.
  
  Source


To further stress the sacred nature of this ordinance:


  The ordinance of the sacrament makes the sacrament meeting the most
  sacred and important meeting in the Church.
  
  Source


Given how sacred the ordinance is, it seems given that children shouldn't be permitted to "play" Sacrament.  For example, constructing their own version of the sacrament from bread and water in the kitchen and then serving to themselves.

However, understanding that young children often imitate things they encounter (these are young children we are talking about here, ages 2, 4, and 5), and that they clearly are not intending any disrespect or irreverence, it could also be looked at as a form of reverence in itself that they want to administer and partake of it as part of their play.  Also, it is something they look forward to each week and there is concern that putting the kibosh on it during playtime at home may suck the fun and excitement out of it.  Children can be particularly susceptible to shaming and guilting, and that does not seem appropriate.  However it does seem important to teach them to respect the ordinance.

Is there anything in LDS teaching that addresses this issue, or is it a matter left entirely to the judgment of parents?
Previous answers speak of small children receiving the Sacrament, rather than imitating it as play.  As for that question,


  Is there anything in LDS teaching that addresses this issue, or is it a matter left entirely to the judgment of parents?


I'm not aware of anything that addresses this issue specifically, but more generally, Latter-Day Saints believe in the doctrine of the Age of Accountability, the concept that little children are not capable of committing sin, (including sacrilege, which is what making light of sacred ordinances would fall under,) until they are mature enough to understand the basic abstract concepts of morality.

Doctrine and Covenants 18:42 states that


  For all men must repent and be baptized, and not only men, but women, and children who have arrived at the years of accountability.


This is further clarified in Doctrine and Covenants 68: 27:


  And their [church members'] children shall be baptized for the remission of their sins when eight years old, and receive the laying on of the hands.


As the question is dealing with children well below the age of eight, there's no real moral problem with it.  Play-acting is one of the ways that children use to come to understand the world around them; a wise parent would not discourage this, particularly for things that they want their children to understand and engage with, such as their faith.