It is good to start thinking about these awkward situations before your child is born. In this way you can help to avoid making the situation more difficult than it needs to be.

First of all, what your parents are doing is quite natural for them. This is a part of their tradition which they want to share with their loved ones. At the same time, they more than likely have no concept of Islam other than what they are exposed to through the media and through you, as they essentially live in a locality that has no or very few Muslims. This is not helped by a media that reports 'banning Christmas" because of the idea that is better to not wish the public "A Happy Xmas", but to wish "A Happy Season", in order to not offend. For those whose tradition it is to celebrate Christmas, it makes them want to hold onto it more despite the general knowledge amongst Christian scholars that Xmas (i.e. 25^th December) has nothing to do with the birth of Prophet Issa (Jesus). In fact he was not born at that time of the year at all!

Your child is to be born within a few days, and what is sure for at least the first year of his life, is that he will be totally unaware of the significance of a reindeer. It will just be a toy from his grandparents that he may or may not play with. Thank them for their considerate gift as this costs you nothing. We are advised:

We should never ridicule the religious beliefs of others, no matter how much we disagree with them:

("And insult not those whom they worship besides God, lest they insult God wrongfully without knowledge. Thus We have made fair-seeming to each people its own doings; then to their Lord is their return and He shall then inform them of all that they used to do" ) (An-Anam 6: 10) 

(" And when you are greeted with a greeting, greet with a better (greeting) than it or return it; surely Allah takes account of all things") (An-Nisa 4: 86).

Let them know in a casual way the importance of Prophet Issa in Islam:

("... We gave Jesus the son of Mary clear arguments and strengthened him with the holy spirit... " )(Al-Baqarah 2: 87)

("And We sent after them in their footsteps Issa, son of Mariam, verifying what was before him of the Tawrat and We gave him the Injeel[The Gospels],in which was guidance and light…" ) (Al Maidah 5: 46)

As your son grows older, of course the situation will become more awkward, but as a Muslim, you should know that what Islam says about not offending your parents regardless of whether they are Muslims or not, still applies. Of course, this is a true test of our faith, i.e. learning how to maintain family relations and your deen, at the same time. The only exception is when what ones parents want would require us from separating from our religion.

("And we have enjoined man in respect of his parents – his mother bears him with faintings upon faintings and his weaning takes two years – saying: Be grateful to Me and to both your parents; to Me is the eventual coming. And if they contend with you that you should associate with me what you have no knowledge of, do not obey them, and keep company with them in this world kindly, and follow the way of him who turns to Me, then to Me is your return…" )(Al-Luqman 14-15)

American convert, Saraji Umm Za`id gave the following advice which applies to relations with non-Mulsim family members not just for festive seasons. It will defintiely help you when akward moments are upon you:

• Allow them time to be pleased with these positive
changes, so that they may see that Islam is for the better, not just
for you, but for all people. If they see that Islam is "good for
you," they may react more positively when you talk with them about
it.

• Make sure that you emphasize that this hasn't changed you in any radical way, and that you strongly desire to keep your relationship with them intact. Make sure that they have access to their grandchildren, but at the same time, make it clear to them that you will not tolerate any attempts to teach them anything other than Islam, or allow them to eat haram foods or participate in haram activities.

• Don't begrudge them for their hurt feelings, and if necessary, allow
them time to work through any issues that they may have: it may go
deeper than your choice to become a Muslim.

• Do not allow yourself to get dragged into a "Christianity vs. Islam," or any sort of interfaith debate with your parents or other family members.

• Ifa family member hurls a "judgment" atyou (e.g., "You're a Satan worshipper who's going to hell!"),  do NOT respond in kind! If your relationship outside of this religious difference is salvageable, then avoid any religious discussions until everyone is willing to discuss it in a more open minded and civilized manner.

• Finally, do not allow yourself to be baited or upset by any "anti-
Islamic" things your parents and family might say.

I pray that you find the above useful, and I wish you a sound and healthy delivery and congratulations in advance.

For your further guidance, please try the following links:

How to Deal With Non-Muslim Mothers
Lying When Speaking to Non-Muslims
When Children Hang-Out With Non-Muslims
Food Prepared By Non-Muslims

Eating Food Made By Non-Muslims
Congratulating Non-Muslims on Festive Occassions

Do you have some suggestions and advice for this sister?  If so, why not let her know in   Christmas With Non-Muslims