Is optimism and positive attitude counterproductive?

Would seeing the bright side of things in life impede me from making spiritual progress?

No it won't. But what do you mean by bright side ? If you mean to say that Buddha is the bright side then it wont impede you from making spiritual progress.

To be able to see good in bad and bad in good is called freedom from circumstances.

Optimism and positive attitude - is it counter productive in Buddhism?

It depends on what is its cause.

If it is caused by greed or lust, aversion and/or delusion, for e.g. you're happy because your craving for chocolate cake was fulfilled, or because the colleague you strongly dislike has resigned and will soon leave your workplace, then it is considered counter productive in Buddhism.

However, if you are optimistic and positive, due to reasons like the following, then it is considered skillful in Buddhism.

From the Dhammapada:

197. Happy indeed we live, friendly amidst the hostile. Amidst hostile men we dwell free from hatred.

198. Happy indeed we live, friendly amidst the afflicted (by craving). Amidst afflicted men we dwell free from affliction.

199. Happy indeed we live, free from avarice amidst the avaricious. Amidst the avaricious men we dwell free from avarice.

200. Happy indeed we live, we who possess nothing. Feeders on joy we shall be, like the Radiant Gods.

Dhammapada 200 refers to piti (rapture) of jhana.

Sometimes being optimistic is useful in particular situations, to help people.

Happy mind tends to be calm, with less vexations; and that helps to put efforts in helping sentient beings, instead of wasting our energy in self-centered vexations.

So it's not advisable to be over-excited with anything, or to attach to anything (because ultimately you can't keep what you are attached to, and so attachments lead to wasting our energy in suffering).

Also, attachments impair the scope of our view.

But if we practice optimism as calm, non-exciting way of living happily, then it helps to keep our perceptions open, unconstrained, and to understand things deeper.

That's why, for example, the practice of dana (giving) helps to develop prajna (wisdom): calm and happy mind is clear and sees well.

As for "not experiencing emotions in nirvana", that sentence can be easily misunderstood.

I would advise you to investigate where it comes from and what it actually means.

There are mistranslations and misconceptions about that even in books of some famous Buddhist teachers.

For example, Khyentse says that "All emotions are painful". However, that's true only for a very specific understanding of the term "emotions", not quite corresponding with what we consider to be emotions in our daily experience.

We can understand "emotions" as just feelings that carry useful signals. It's a part of our mental abilities, and there is nothing wrong with them.

Only when they become attached to, problems start to arise.

In nirvana — phenomena happen, including emotional phenomena; trying to "get rid of emotions" might be a wrong kind of practice.

Good householder, optimism and positive attitude is counterproductive (in regard of long lasting happiness) if the objects are in the world, object of sense. Joy, optimism, positive attitude toward awakening, skillful deeds... called "pasada" and arising after Saddha, which arises after Dukkha, are very needed tools to gain piti and the rest of releasing path till highest liberation, the Ariya-path. In short, all optimism and positive attitude toward that of what is actually subject of decay isn't smart, nurishes causes for suffering.

Useful talk on things less known here: Affirming the Truths of the Heart: The Buddhist Teachings on Samvega & Pasada

May good householder have enough optimism and positive attitude to investigate here deeper and trust that it will be for his long term happiness.

Getting a human existance, meeting the Tripple Gems, go after it, such is indeed a bright life and it's actually cause, if meeting Dukkha together with the path for release, for highest happiness, Unbound. So one needs to rejoice actually with such a life, such a gain, meeting such possibilities, hard ever to meet.

Therefore mudita has to start with oneself (=anussati)

[Note that this isn't given for stacks, exchange, worldbinding trades but toward release from it.]