A couple of factors such as their exposure to early mathematics and problem solving  would be the determinant to enable students to solve mathematical problems at an early age.  

Critical thinking taught at an early age can do the trick. But personally, sheer perseverance has enabled me to solve certain mathematical problems.

One other thing i'd like to add is that some some students are born with very high I.Q.s  and can solve really challenging questions with ease.

Read the works of Prof. Carol Dweck of implicit theory.

Implicit theory means the one believes about his own ability: either fixed for developed. If he believes that his ability (intelligence) is fixed, then he will see no meaning to face challenging tasks more than his "fixed ability". This will grow to make him avoid new tasks after any successful challenge (including learning new things).....

Please refer to Prof. Carol Dweck's work. Her works are full of supporting evidences, in specifically in mathematics.

Motivation is the best thing which can enable higher order thinking skills among students to solve mathematical problems by their experiences.

Students' lack of adequate basic skills and knowledge affect their progress in learning more advanced problem solving mathematics.  For example, I have noted where I am that high school students depend on a calculator for any calculation including basic facts of addition, subtraction and multiplication. How can they do more advanced maths in such situations 

At my current university, historical factors and a weak foundation coupled with the way the students 'learn' mathematics  affects the logical thinking and problem solving skills of many students.

The answers regarding Dweck's & Schoenfeld's work are good starting places.  I would add to the list:

• epistemic beliefs (the nature of knowledge or intelligence)

• domain specific epistemic beliefs (math

   problems are solved quickly or not at all)

• motivation (namely interest in solving the problem

   & self-efficacy to believe it can be done)

• volition (the ability and/or desire to persist thru

   to a solution, relating to ExV theory)

• creativity (the often overlooked element of critical thinking)

A number of the responses above have addressed potential hurdles that students may encounter (e.g., past preparation or performance and innate talents).  However, I am uncertain that these help answer your query:  ¿What enables students to successfully problem solve using HOT skills?  Whereas a further exploration of the elements I've listed would (ideally) help support nearly any student attempting such problem solving activities.

Taking the aforementioned answers into account, I would like to add, that the answer depend on the issues how to define higher order thinking skills and what is your "belief" about the nature of mathematics.

E. g., taking the problems from international math olympics, there should be given (motivation and curiosity should be in any case a necessary condition) flexibility and security in standard techniques as  mathematical induction, different forms of proofs, pigeon-hole principle, manipulation of symbolic expressions (cf. e.g. A. Engel (1998) Problem-solving strategies. Springer).

But if you place a stronger emphasis on mathematical creativity and simulation of real mathematical research processes,  students should have a stronger interest in inventing new problems and litlle mathemtaical theories. Cf. e.g. Wagner, H., & Zimmermann, B. (1986). Identification and fostering of mathematically gifted students. Rationale of a pilot study. Educational Studies in Mathematics, August 1986, Volume 17, Issue 3, pp 243-260

These approaches are, of course, not disjoint, but one should be aware, that even mathematics is not value-free and one has to detect and decide one's own approach counsciously.

Thank you very much for all the answers and ideas given and it really gives me a wonderful perspective of the issue In hand. There are lots of theories regarding it and it seems endless.... however it would be wonderful if we can share our own experiences as an educator watching children/students  solve problems and what makes a children differs from one another when it comes to their skills of solving a particular HOTS problem. From my experience as an educator, cultural background seems to be one of the factors that differentiate their views of understanding and solving the problem. Does this resonates with anyone else?    

The tools that are available also impact on students' mathematical problem solving. In a recent project we looked at what middle school students (aged 10-14) could do when solving mathematical problems outside school as part of a mathematics competition; see the recent book:

Carreira, S., Jones, K., Amado, N., Jacinto, H., & Nobre, S. (2016). Youngsters solving mathematical problems with technology: The results and implications of the Problem@Web Project. New York: Springer

http://www.springer.com/gb/book/9783319249087

Cultural background  might be one the factors since its connected with ones epistem8c belief. Though other factors thats i perceived quite demonstrated among students who are good in problem solving are their urge of inquiry in their thoughts and ability to conceptualize the mathematical concepts involved in the problem to make sense to them. 

I think with Schoenfeld and DeCorte two of the most prominent frameworks have already been given. There is also interesting quantitative work by Chinnappan, Ekanayake, & Brown (2011) Specific and General Knowledge in Geometric Proof Development  that point to various factors.

Taking a broader perspective, also literature on scientific thinking / reasoning would be a good place to look at. Examples would be:

Deanna Kuhn (2002) What is scientific thinking, and how does it develop

Corinne Zimmermann (2000) The Development of Scientific Reasoning Skills

Answering also experience directed, gut feeling part of the question: I think that student beliefs about mathematics and the sort of problem solving they are supposed to do is a really important factor, although I think that many other factors (e.g. domain-specific knowledge or knowledge about heuristics) are easier or at least faster to foster / change in a desirable direction.