Yes the first one is fine, and is quite common. This is romantic. Just "give me a hug, or come and hug me" . These are not romantic, simply friendly gestures Embrace is used in a number of contexts, as in he embraced the idea, it is rarely used in a romantic context.

我不是很赞同另外两位参与者的解释，当然可能只是每个人的理解有所不同，但按我个人的感觉，cuddle与hug并没有区别，就是有的人可能多习惯于用前者，有的多习惯于用后者。然而，a kiss and a cuddle是一个约定俗成的较为固定的片语，因此虽然改成a kiss and a hug没有错误，但没有前者地道顺耳。至于embrace这个词呢，它较为形象地代表接抱于怀中，多用于正式场合，也可以引申为接受一个概念等抽象的东西之意。Give me a kiss and a cuddle很地道，很妥当，可以理解为“亲一下，抱一下”，kiss me and hug me反而听起来有点别扭，作为祈使语气听起来有点过分或迫切的感觉，然而用于叙述语句中合适，当然动词的形式得符合语法的要求。

A hug refers to when you put your arms around someone briefly and then let go, and can be done to express affection or to offer comfort. To cuddle implies affection and is not generally used in the context of giving comfort. A hug is a relatively short event. A cuddle lasts a lot longer. Family and friends usually get a hug (short time), while the one you love gets an embrace (long time and intimate). Another definition of embrace: to encircle and hold onto, as embracing an idea or thought. hug is just physical embrace- you welcome somebody eniterly.