Do arena entrances or card pack prices ever change?

Hearthstone card packs are 100 gold per pack. An entrance to the arena costs 150 gold. Have these prices ever temporarily been reduced for a sale or special? Has there been any mention of sales by Blizzard?

As of now, there has been no such announcement. As far as my memory reaches, the pack price has also not changed.

What has changed, though, is the Arena price. Originally (early closed beta), the Arena was called "The Forge" and required actual packs as an entrance fee instead of gold. In exchange, you would keep all the cards you drafted. And the rewards were also different. But since this was an early beta experiment, it's probably safe to assume they like it better the way it is now and won't change it again (especially since beta is over).

If we look at other big freemium games, we can see that there are frequently sales or special offers, but they usually affect real money prices only. So even if there will be such a sale or offer one day, it probably won't change the gold price, but instead alter the gold-to-money ratio.

Using the Amazon App Store, there is now currently a discount on packs. Amazon is offering bonus 'coins' (their currency) for buying things, and doing so can net you lots of extra value if you're willing to spend real money on Hearthstone. This reddit thread describes the methods for attaining the discount:

1. Be using an Android tablet. If you don't have one, you can borrow a friend's tablet for 10-15 minutes.
2. If Hearthstone is already installed, but was installed via Google Play, uninstall it. Install the Amazon App Store if you don't already have it.
3. Use the Amazon App Store to install Hearthstone.
4. Open Hearthstone, go to the store, be sure to select the correct type of card pack (wink), select 40 packs, and click Buy.
5. Immediately look for the note indicating that this purchase earns 2500 bonus coins. This offer could expire at any time, Blizzard did not specify when this offer might expire. Don't hold it against me if the note is gone and you don't get the discount. Make sure it's there!
6. When asked to select a payment method, notice the option to pay with Amazon coins. Click the link to "Buy more" coins. Choose the option to buy 10,000 coins for $80.
7. Once you have your 10,000 coins, use them to buy packs. 40, 40, 40, 15, 7, and 2. Make sure to buy them in that order so you earn your bonuses first.